Photo credit: Anna Logue

Research activities

Find out more about the Chair in Applied Analysis' research activities throughout the years.

  • 2019

    23.07 Rate of convergence towards Hartree dynamics

    Title: Rate of convergence towards Hartree dynamics
    Speaker: Lee Jinyeop (KAIST)
    Abstract: We consider interacting $N$-bosons in three dimensions. It is known that the difference between the many-body Schrödinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$. We investigate

    • the rate of convergence for more singular interaction potential,
    • the time dependence of the difference, and
    • the rate of convergence for mixture condensation with $p$-components.

    To the investigation, we will review quantum mechanics briefly from very basic ideas to the concept of Bose-Einstein condensation. Moreover, to introduce the main technique of the proof, we will also cover the basics of Fock space representation. Strichartz estimate and time decay estimate are main new analytic tools for the proof.

    Date: 23 July 2019 (Tues)
    Time: 10:00 - 11:30
    Location: TBA

     

    11.07 The Global dynamics on 1D compressible MHD

    Title: The Global Dynamics on 1D compressible MHD
    Speaker: Ronghua Pan (Geogia Institie of Technology)
    Abstract: Global dynamics of classical Solutions of 1D Compressible MHD with large initial data has an interesting history and is challenging. We will report a recent Progress made by my Joint work with X. Qin.

    Time: 16:00-17:30, 11.07.2019

    Place: B6 A303

     

    11.07 Multi-species cross-diffusion population models: existence of solutions and derivation from underlying particle models (Esther Daus)

    Title : Title: Multi-species cross-diffusion population models: existence of solutions and derivation from underlying particle models
    Speaker: Esther Daus (TU Wien)
    Abstract : In the first part of this talk, we focus on the proof of the existence of global-in-time weak solutions to reaction-cross-diffusion Systems for an arbitrary number of competing population species. In the case of linear transition rates, the model extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a  detailed balance or weak cross-diffusion condition, where the detailed balance condition is related to the  symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. The second part of the talk links at the formal level the entropy  structure of the cross-diffusion system satisfying the detailed balance condition  with the entropy structure of a reversible microscopic many-particle Markov process on a discretised space. Moreover, we  present a very recent proof of a rigorous mean-field limit from a  stochastic particle model to a cross diffusion model. These results are based on a joint work with Xiuqing Chen and Ansgar Juengel,  a Joint work with Helge Dietert and Laurent Desvillettes, and a joint work with Li Chen and Ansgar Juengel.

    Time: 14:30-16:00, 11.07. 2019

    Place: B6 A303

     

    11.07 Random horizon principal-agent problem (Junjian Yang)

    Title : Random horizon principal-agent problem
    Speaker: Junjian Yang (TU Wien )
    Abstract :We consider a general formulation of the principal-agent problem with a continuous payment and a lump-sum payment on a random horizon. We first find the contract that is optimal among those for which the agents value process allows a dynamic programming representation, in which case the agents optimal effort is straightforward to find. We then show that the optimization over this restricted family of contracts represents no loss of generality. Using this approach, we reduced a non-zero-sum stochastic differential game to a stochastic control problem which may be solved by standard methods of stochastic control theory. At the beginning of the talk, I will also give an overview about the interplay between PDE and 
    stochastics.

    Time: 13:00-14:30, 11.07. 2019

    Place: B6 A303

  • 2018

    13.12 Logarithmic delays in non local Fisher KPP problems. (Emeric Bouin)

    Title : Logarithmic delays in non local Fisher KPP problems.
    Speaker: Emeric Bouin (Université Paris-Dauphine)
    Abstract : We consider the non-local Fisher-KPP equation modeling a population with individuals competing with each other for resources with a strength related to their distance, and obtain the asymptotics for the position of the invasion front starting from a localized population. Depending on the behavior of the competition kernel at infinity, the location of the front is either as in the local case, or polynomial. This is a joint work with Christopher Henderson (U. Chicago) and Lenya Ryzhik (Stanford).

    Time: 10:15-11:45, 13.12. 2018

    Place: C116

     

    24.10 Well/ill posedness for problems in fluid mechanics (Eduard Feireisl)

    Title: Well/ill posedness for problems in fluid mechanics
    Speaker: Eduard Feireisl (Institute of Mathematics AS CR )
    Abstract: We discuss the state of the art of well/ill posedness of problems 
    arising in dynamics of compressible viscous/inviscid fluids. We propose 
    a solution to this problem based on stochastic approach selecting a 
    suitable Markovian semigroup.

    Time: 11:00-12:30

    Place: B 6, A 303

     

    27.02 Effective equations for focusing bosonic systems (Thanh Nam Phan)

    Title: Effective equations for focusing bosonic systems
    Speaker: Thanh Nam Phan (LMU)
    Abstract: We study the effective descriptions of many-body Schroedinger dynamics of interacting bosons. To the leading order, the system exhibits the Bose-Einstein condensation and the condensate is described by a one-body nonlinear  Schroedinger equation. To the second order, the excitations around the condensate are effectively described by Bogoliubov theory. I will discuss some recent results on the rigorous derivation of the effective equations. A special attention will be paid on the focusing case, where the stability of the system is not obvious.

    Time: 10:15-11:45 27.02.2018

    Place: C116, A5,6

     

    24.01 Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system (Johannes Lankeit)

    Title: Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system
    Speaker: Johannes Lankeit (Paderborn)
    Abstract: We consider a parabolic-elliptic chemotaxis system generalizing
       \[ \begin{cases}\begin{split}
    & u_t=\nabla\cdot((u+1)^{m-1}\nabla u)-\nabla \cdot(u(u+1)^{\sigma-1}\nabla v)\\
    & 0 = \Delta v - v + u
       \end{split}\end{cases} \]
    in bounded smooth domains $\Omega\subset \mathbb{R}^N$, $N\ge 3$, and with homogeneous Neumann boundary conditions. We show that
       *) solutions are global and bounded if ${\sigma}    *) solutions are global if $\sigma \le 0$
       *) close to given radially symmetric functions there are many initial data producing unbounded solutions if $\sigma >m-\frac{N-2}N$.
       In particular, if ${\sigma}\le 0$ and $\sigma > m-\frac{N-2}N$, there are many initial data evolving into solutions that blow up after infinite time.

    Time: 24.01.2018   14:00-15:30

    Place: A5 6, C116

     

    10.01 Global existence analysis of cross-diffusion population systems for multiple species (Esther Daus)

    Title: Global existence analysis of cross-diffusion population systems for multiple species
    Speaker: Esther Daus (TU Wien)
    Abstract: We prove the existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction), the entropy is nonincreasing in time, but co­unter-examples show that the entropy may increase initially if detailed balance does not hold.

    This is a joint work with X. Chen and A. Juengel.

    Time: 10.01.2018  9:00-10:30

    Place: A5 6 C116

  • 2017

    19.12 Stability of Compressible Navier-Stokes/Euler-Maxwell systems (Yuehong Feng)

    Title: Stability of Compressible Navier-Stokes/Euler-Maxwell systems
    Speaker: Yuehong Feng (Beijing)
    Abstract: In this talk, we give the long time decay rates and stabilities of solutions for Euler/Navier-Stokes-Maxwell systems, which are partial differential equations arising from plasmas. My talk is essentially composed of three parts dealing with Cauchy problems and periodic problems. In the first part, we study the long time  decay rates  of the global smooth solutions for compressible Euler-Maxwell systems in non isentropic case when the equilibrium solutions are constants. In the second part, we consider the stabilities of smooth solutions near non constant equilibrium states for the compressible Euler-Maxwell systems. In part three, we investigate the global existence near constant equilibrium states and the stability of smooth solutions near non constant equilibrium states for the compressible Navier-Stokes-Maxwell systems, respectively.

    Time: 19.12.2017 12:30-13:30

    Room: A5 C116

     

    15/16. 12. Mini-Worshop: Effective equations for many particle Coulomb system

    15.12.2017-16.12.2017,    A5 6, C012

    15.12.2017 Afternoon

    Speaker

    Topic

    14:30-15:20

    Merz

    On the Atomic Density on the Semiclassical Length Scale in

    Relativistic Quantum Mechanics

    15:20-16:10

    Griesemer

    On the dynamics of polarons in the strong-coupling limit

    16:10-16:40

    Coffee break

    16:40-17:30

    Morozov

    Fourier-Mellin theory of the relativistic massless Coulomb operator

     

    16.12.2017 Morning

     

     

    9:00-9:50

    König

    Classification of positive solutions to a
    nonlinear biharmonic equation with critical exponent

    9:50-10:40

    Chen

    An inequality on the inverse of |x| projected to the positive spetral

    subspace of the free Dirac operator: with applications to the

    ionization problem of the Brown-Ravenhall operator

    10:40-11:10

    Coffee break

     

    11:10-12:00

    Liew

    Hewitt-Savage Theorem and its application in Fermionic semi-classical measures on phase space.

     

    16.12.2017 Afternoon

     

     

    14:00-14:50

    Wang

    Some PDEs with competition effects and functional inequalities

    14:50-15:40

    Cuenin

    Embedded eigenvalues of generalized Schrödinger operators

    15:40-16:10

    Coffee break

     

    17.10 Understanding blood cancer dynamics - insights from mathematical modeling (Thomas Stiehl)

    Title: Understanding blood cancer dynamics - insights from mathematical modeling
    Speaker: Thomas Stiehl (Institute of Applied Mathematics, Heidelberg University)
    Abstract: Acute leukemias are cancerous diseases of the blood forming (hematopoietic) system. The leukemic cell bulk is derived from a small and heterogeneous population of leukemic stem cells. Upon expansion, the leukemic cells out-compete healthy blood production which results in severe clinical symptoms. To study the interaction of leukemic and healthy cells, we propose mathematical models of hierarchical cell populations. Cell competition and selection are mediated by various biologically inspired feedback mechanisms. The models relate disease dynamics to basic cell properties, such as proliferation rate (number of cell divisions per unit of time) and self-renewal fraction (probability that a progeny of a stem cell is again a stem cell). Depending on the posed questions, we use different mathematical approaches, including nonlinear ordinary differential equations, integro-differential equations and stochastic simulations.

    A combination of mathematical analysis, computer simulations and patient data analysis provides insights in the following questions:

    1. Which mechanisms allow leukemic cells to out-compete their benign co­unterparts?
    2. How do leukemic stem cell properties (proliferation rate and self-renewal fraction) affect the clinical course and patient prognosis?
    3. What can we learn about leukemic stem cell parameters using routine clinical data?
    4. What is the impact of leukemic stem cell heterogeneity on disease dynamics? Which cell properties confer selective advantages?
    5. How do leukemic cells respond to signals from their environment? Does this affect disease dynamics?

    The talk is based on joint works with Anna Marciniak-Czochra (Institute of Applied Mathematics, Heidelberg University), Anthony D. Ho, Natalia Baran and Christoph Lutz (Heidelberg University Hospital).

    Time: 17.10.2017,  12:00-13:30

    Room: A5 C116

     

    16.08 Nonlinear Evolutionary Systems and Green's Function (Weike Wang)

    Title: Nonlinear Evolutionary Systems and Green's Function
    Speaker: Weike Wang (Shanghai Jiao Tong University)
    Abstract: In this talk, I will show how real analysis and Green’s function method are applied for pointwise estimates of nonlinear evolutionary systems. Especially, for compressible Navier-Stokes equations, the general Huygan’s principle is obtained. I will also combine the Green’s function method and energy method to solve the initial-boundary value problem.

    Time: 16.08.2017 14:30-16:00

    Room: B139, A5

     

    19.07 Mean-field limit for the Keller-Segel system and the theory of propagation of Chaos (Hui Huang)

    Title:Mean-field limit for the Keller-Segel system and the theory of propagation of Chaos
    Speaker: Hui Huang (Tsinghua University)
    Abstract:We study the propagation of chaos for the N-particle chemotaxis system subject to the Brownian diffusion. More precisely, we present a probabilistic proof of the distance between the exact microscopic and the approximate mean-filed dynamics, which leads to a derivation of the Keller-Segel equation from the microscopic N-particle system.

    Time: 17.07.2017, 14:00-15:30

    Room: A5 C116

     

    17.07 Fractional Laplacian and the Keller-Segel system with the nonlocal diffusion (Hui Huang)

    Title:  Fractional Laplacian and the Keller-Segel system with the nonlocal diffusion.
    Speaker: Hui Huang (Tsinghua University)
    Abstract: In this talk, I will give a brief introduction of the fractional Laplacian and describe our work of the Keller-Segel system subject to the Levy diffusion.

    Time: 17.07.2017, 14:00-15:30

    Room: A5 C116

     

    05.07 Dissipative reaction diffusion systems with quadratic growth (Takashi Suzuki)

    Title: Dissipative reaction diffusion systems with quadratic growth
    Speaker: Takashi Suzuki (Osaka)
    Abstract: We introduce a class of reaction diffusion systems of which weak solution exists global-in-time with relatively compact orbit in L1. Reaction term in this class is quasi-positive, dissipative, and up to with quadratic growth rate. If the space dimension is less than or equal to two, the solution is classical and uniformly bounded. Provided with the entropy structure, on the other hand, this weak solution is asymptotically spatially homogeneous. Joint work with Michel Pierre and Yoshio Yamada.

    Time: 05.07.2017, 14:00-15:30

    Room: A5 C116

     

    03.05 On the regularity of the 3D Navier-Stokes equations (Daoyuan Fang)

    Title:  On the regularity of the 3D Navier-Stokes equations
    Speaker: Daoyuan Fang (School of Mathematics Sciences, Zhejiang University)
    Abstract: In this talk, I will show some recent results on the 3D Navier-Stokes equations, which were obtained by our group during these years.

    Time: 03.05.2017, 10:30-12:00

    Room: A5 C116

     

    15.03 Propagation of chaos for the Vlasov-Poisson system (Phillip Grass)

    Title:  Propagation of chaos for the Vlasov-Poisson system
    Speaker: Phillip Grass (LMU)
    Abstract: The Vlasov equation is used to describe the macroscopic time evolution of a system consisting of many particles interacting by newtonian dynamics. In case of singular interaction a rigorous proof justifying this approach can be very challenging and is still an open problem for the most interesting case which is coulomb interaction. The desired result is to show that for typical initial conditions the empirical density given by the positions of the particles in phase space converges to the solution of Vlasov equation. In this talk, I will introduce a method recently developed by Boers, Lazarovici and Pickl which allows to consider the coulomb case with some cut-off depending on the particle number $N$. Additionally, I will suggest some adaptions to this approach which can be helpful to shrink the size of the $N$-dependent cut-off.

    Time: 15.03.2017, 10:30-11:30

    Room: A5 C116

     

    03.03 Nonlinear aggregation-diffusions in the diffusion-dominated and fair-competitions regimes (Jose Carrillo)

    Title: Nonlinear aggregation-diffusions in the diffusion-dominated and fair-competitions regimes
    Speaker: Jose Antonio Carrillo (Imperial College, London)
    Abstract: We analyse under which conditions equilibration between two competing effects, repulsion modelled by nonlinear diffusion and attraction modelled by nonlocal interaction, occurs.  I will discuss several regimes that appear in aggregation diffusion problems with homogeneous kernels. I will first concentrate in the fair competition case distinguishing among porous medium like cases and fast diffusion like ones. I will discuss the main qualitative properties in terms of stationary states and minimizers of the free energies. In particular, all the porous medium cases are critical while the fast diffusion are not. In the second part, I will discuss the diffusion dominated case in which this balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrisation techniques. Calculus of variations tools allow us to show the existence of global minimizers among these equilibria. Finally, in the particular case of Newtonian interaction in two dimensions they lead to uniqueness of equilibria for any given mass up to translation and to the convergence of solutions of the associated nonlinear aggregation-diffusion equations towards this unique equilibrium profile up to translations as time tends to infinity. This talk is based on works in collaboration with S. Hittmeir, B. Volzone and Y. Yao and with V. Calvez and F. Hoffmann. 

    Time: 03.03.2017, 15:30-16:30

    Room: C116

     

    22.02 Quantitative Isoperimetric Type Inequalities and Applications (Giovanni Pisante)

    Title: Quantitative Isoperimetric Type Inequalities and Applications
    Speaker: Giovanni Pisante (University of Campania “Luigi Vanvitelli”)
    The simplicity in the statement of the isoperimetric inequality, together with the subtle difficulties that its rigorous proof hid, had been a source of increasing interest for mathematicians. In the past decades several quantitative versions and many related applications have been presented, often with more than one proof. Aim of the lectures is to give an introduction to the classical isoperimetric inequality and to various stability results proved in recent years for this inequality and other related geometric and analytic inequalities.

    Time: 22.02.2017, 10:15-11:45

    Room: A5 C116

     

    15.02 On the selection of solutions to a nonlinear pde system (Giovanni Pisante)

    Title:  On the selection of solutions to a nonlinear pde system
    Speaker: Giovanni Pisante (University of Campania “Luigi Vanvitelli”)
    In the last decades a great effort has been devoted to the study of nonlinear systems of partial differential equations of implicit type. Different and quite general methods have been developed to prove the existence of almost everywhere Lipschitz regular solutions. The usual approaches are not constructive and usually, when they can be applied, provide the existence of infinitely many solutions. Thus the question of selecting a preferred solution among them raised. In the recent literature some selection criteria have been proposed to somehow minimize the irregularities of the solutions to scalar problem.

    The aim of the talk is to propose a selection criterion for a particular 2-dimensional vectorial problem, hoping to shade some light on the different difficulties that one can enco­unter when passing from the scalar to the vectorial case. We provide a variational method to select, among the infinitely many solutions, the ones that minimize an appro- priate weighted measure of some set of singularities of the gradient. The talk is based on a recent joint work with G. Croce. 

    Time: 15.02.2017, 10:15-11:45

    Room: A5 C116

     

    08.02 Duality approach for some variational problems involving polyconvex integrands (Giovanni Pisante)

    Title:  Duality approach for some variational problems involving polyconvex integrands
    Speaker: Giovanni Pisante (University of Campania “Luigi Vanvitelli”)
    Duality methods have beed proved to be a very useful tool in the Theory of Calculus of Variations. The theory is however fully developed only in the convex setting. Several attempts have been made to try to generalize the method to non-convex problems. Aim of the talk is to present an approach that has been recently proposed to identify dual problems for a class of polyconvex integral functionals and to discuss how this theory can be successfully applied to recover informations on the minimizers

    Time: 08.02.2017, 10:15-11:45

    Room: A5 C116

  • 2016

    06.12 Infinite mass boundary conditions for Dirac operators and its relation to graphene (Edgardo Stockmeyer)

    Title:  Infinite mass boundary conditions for Dirac operators and its relation to graphene
    Speaker: Edgardo Stockmeyer (Institute of Physics, PUC, Chile)
    Abstract: In this talk I will review some recent results on certain Dirac operators defined on a planar domain . In particular, we will present some basic spectral properties of these operators for different boundary conditions and will discuss its relation to graphene flakes. Moreover, for some particular boundary conditions, I will show that the corresponding operator is the limit, as M ! 1, of a Dirac operator defined on the whole plane, with a mass term of size M supported outside.

    Time: 6.12.2016, 14:00-15:00

    Room: A5 C116

     

    01.12 On a class of cross diffusion problems arising in population dynamics (Laurent Desvillettes)

    Title:  On a class of cross diffusion problems arising in population dynamics
    Speaker: Laurent Desvillettes (Paris)
    Abstract: We are going to discuss about systems of reaction-cross diffusion equations arising in population dynamics. The mechanism of cross diffusion has been introduced by Shigesada Kawasaki and Terramoto to model the trend of a species to avoid another one and thereby, possibly segregate. The equations model the evolution of individuals belonging to two species in competition, which increase their diffusion rate in order to avoid the individuals of the other (or the same) species. More precisely, we will discuss about new results on the uniqueness, well-posedness, existence and non-existence of weak solutions to such parabolic problems and systems.

    Time: 01.12.2016, 14:00-15:00

    Room: A5 B139

     

    14.11 Transport models of data flows in high performance computing (Richard C. Barnard)

    Title:  Transport models of data flows in high performance computing
    Speaker: Richard C. Barnard (Oak Ridge National Laboratory USA)
    Abstract: Scientific computing in high performance computing environments is characterized by distributing over many processors a task which is then performed by iteratively performing subtasks on each processor/node and then performing a communication step.  We are interested in  developing  a predictive model for the performance of computations in large/extreme-scale systems which arises from a discrete description of these processes. This talk will discuss the derivation of a continuum model of these systems, taking the form of a nonlinear multi-dimensional transport equation.  We will discuss some theoretical and numerical challenges associated with the model as well as some possible directions for dynamic optimization problems.

    Time: 14.11.2016, 10:00-11:00

    Room: A5 C116

     

    Oct. 22 and 23, Analysis workshop

    Effective one-particle equations for fermionic many-particle Coulomb system: derivation and properties.
    The focus of this meeting is to get people from three working groups (LMU and Uni-Mannheim) together and to concentrate on the derivation and properties of the effective one-particle equations for (fermionic) many particle systems. The emphasis will be on electrons that interact via Coulomb forces among each other and the nucleus. Both, the stationary and the dynamic case will be discussed. In the stationary case the emphasis will be on relativistic Coulomb systems.  In the dynamical case, there are few results for Coulomb systems even in the non-relativistic setting. Some of the known results will be presented and further development of mathematical methods which allow the treatment of Coulomb singularities will be discussed. Finally, the effective one-particle equations both in the mesoscopic level (Vlasov type) and hydrodynamic level (Euler-Poisson type) will be introduced and further discussion on the  difficulties resulted from external attractive Coulomb case will be carried out.

    Schedule

    October 22

    9:00-10:30  Konstantin Merz (LMU) Die atomare Dichte auf der Skala  

    10:30-12:00  Heinz Siedentop (LMU)  Die starke Scottvermutung

    14:00-15:30  Peter Pickl (LMU)  Mean field limits for Fermions

    15:30-16:15 Francis Nier (Paris 13) Mean field quantum problems as semiclassical limits: a review

    16:15-17:00  Sergey Morozov (LMU) Lower bound on the modulus of Dirac-Coulomb operators by fractional Laplacians

    17:00-17:30 Discussion session “On possible development of mathematical methods in dealing with additional attractive Coulomb potential”, led by Hongshuo Chen (LMU)

    October 23

    9:00-10:30 Qitao Yin (Mannheim) On the Vlasov-Poisson system

    10:30-12:00 Li Chen (Mannheim) Solvability of the Euler-Poisson system

    Room:  A5,6  C012

     

    27.09 Characterising path-independence of Girsanov transform for stochastic differential equations (Jianglun Wu)

    Title:  Characterising path-independence of Girsanov transform for stochastic differential equations
    Speaker: Jianglun Wu (Swansea, UK)
    Abstract: This talk will address a new link from stochastic differential equations (SDEs) to nonlinear parabolic PDEs. Starting from the necessary and sufficient condition of the path-independence of the density of Girsanov transform for SDEs, we derive characterisation by nonlinear parabolic equations of Burgers-KPZ type. Extensions to the case of SDEs on differential manifolds and the case od SDEs with jumps as well as to that of (infinite dimensional) SDEs on separable Hilbert spaces will be discussed. A perspective to stochastically deformed dynamical systems will be briefly considered.

    Time: 27.09.2016, 14:00-15:00

    Room: A5 C116

     

    20.07 Pseudo-parabolic equation with small perturbation (Y. Cao)

    Title: Pseudo-parabolic equation with small perturbation
    Speaker: Yang Cao (Dalian University of Technology)

    Time: 20.07.2016, 9:30-10:30

    Room: A5 B143

     

    03.05 Acceleration in reaction-diffusion equations (Christopher Henderson)

    Title: Acceleration in reaction-diffusion equations
    Speaker: Christopher Henderson (ENS de Lyon)
    Abstract: Widely used in mathematical biology, reaction-diffusion equations, and in particular the Fisher-KPP equation, are used to model the spreading of a population through a new environment.  The earliest results showed that populations moved at a constant speed (i.e. linear in time).  However, about five years ago, Hamel and Roques discovered acceleration, or super-linear in time propagation of the population, when the initial population is very spread out.  Over the last few years, acceleration has been discovered in a number of other settings.  In this talk, I will discuss several of these settings, with the aim of developing an intuition for what causes and what blocks acceleration.  The work in this talk is joint with Emeric Bouin and Lenya Ryzhik.

    Time: 03.05.2016, 14:00-15:00

    Room: A5 C116

     

    19.04 On existence results for finite energy weak solutions to a class of Quantum Hydrodynamic systems (Paolo Antonelli)

    Title: On existence results for finite energy weak solutions to a class of Quantum Hydrodynamic systems
    Speaker: Paolo Antonelli (L'Aquila)
    Abstract: Quantum Hydrodynamic models arise in the description of superfluid, Bose-Einstein condensates, or in the modeling of semiconductor devices. I will discuss some existence results for finite energy weak solutions, globally in time. By using the underlying wave function dynamics and a polar factorisation technique, which circumvents the use of the WKB ansatz, we are able to set up a consistent theory in terms of mass and current densities, without the need to define the velocity field in the vacuum region. I will then present some recent progresses about models for quantum fluids with self-generated electromagnetic fields and I will try to discuss the open problems in this direction.

    Time: 19.04.2016, 14:00-15:00

    Room: A5 C116

     

    05.04 Derivation and analysis of a system modeling the chemotactic movement of hematopoietic stem cells (Maria Neuss-Radu)

    Title:  Derivation and analysis of a system modeling the chemotactic movement of hematopoietic stem cells
    Speaker: Maria Neuss-Radu (Erlangen)
    Abstract: It has been shown that hematopoietic stem cells migrate in vitro and in vivo towards a gradient of a chemotactic factor produced by stroma cells. In this paper, a mathematical model for this process is presented. The model consists of chemotaxis equations coupled with an ordinary differential equation on the boundary of the domain and subjected to nonlinear boundary conditions. The existence and uniqueness of a local solution is proved and the model is simulated numerically. It turns out that for adequate parameter ranges, the qualitative behavior of the stem cells observed in the experiment is in good agreement with the numerical results. 

    Time: 05.04.2016, 14:00-15:00

    Room: A5 C116

     

    02.03 Three seminar talks on fluid dynamic systems

    Title: Global Well-Posedness for a Model of Incompressible Navier-Stokes in Three Dimensions
    Speaker: Shuguang Shao (Beijing)

    Time: 02.03.2016, 12:30-13:15

    Room: A5 B139

     

    Title: Axially Symmetric Incompressible Flow of Three-dimensional Magnetohydrodynamics
    Speaker: Jihui Wu (Beijing)

    Time: 02.03.2016, 13:15-14:00

    Room: A5 B139

     

    Title: The Solution of a Quasilinear Differential Equation with Closed Non-convex Initial Discontinuity
    Speaker: Haiping Niu (Beijing)

    Time: 02.03.2016, 14:15-15:00

    Room: A5 B139

     

    23.02 Sign-Changing Two-Peak Solutions For An Elliptic Free Boundary Problem Related To Confined Plasmas (Giovanni Pisante)

    Title: Sign-Changing Two-Peak Solutions For An Elliptic Free Boundary Problem Related To Confined Plasmas
    Speaker: Giovanni Pisante (Napoli)
    Abstract: Motivated by the description of equilibrium states for plasmas in a tokamak, we consider a singular problem defined on a planar domain that generalizes the classical model for plasma confinement. This problem shares some structural similarities with the equation describing the desingularized solutions for the Euler equation of two point vortices with opposite signs and it is well known that in these type of problems there is a strong connection between the existence of roughly saying ``bubbling solutions'' and the critical points of the associated Kirchoff-Routh type functional. The aim of the talk is to show how to exploit this relation to prove, via a perturbative method, the existence of solutions with two opposite-signed sharp peaks and to establish some physically relevant qualitative properties for such solutions. These are results from a recent project in collaboration with Tonia Ricciardi (Univ. „Federico II“ in Naples).

    Time: 23.02.2016, 14:00-15:00

    Room: A5 C116

     

    17.02 Effective one particle equations II (H. Siedentop)

    Title: Effective one particle equations II
    Speaker: Heinz Siedentop (LMU)

    Time: 17.02.2016, 14:00-15:00

    Room: A5 C116

  • 2015

    09.12 Incompressible limits (Michael Dreher)

    Title: In compressible limits
    Speaker: Michael Dreher (Heriot-Watt University Edinburgh)

    Time: 09.12.2015, 15:00-16:00

    Room: B139

     

    26.11 The Self-Organized Hydrodynamics models with density dependent velocity (Hui Yu)

    Title: The Self-Organized Hydrodynamics models with density dependent velocity
    Speaker: Hui Yu (Aachen)
    Abstract: We propose a self-organized hydrodynamics model whose velocity depends on the local density. The analysis shows that the correlation between velocity and the local density is essential to the stability. The results are demonstrated by numerical simulations of the particle and the hydrodynamic models with several experimental functions that define the relation between density and velocity. The growth rate of the unstable modes are analysed among the particle, linearized and nonlinear hydrodynamic models.

    Time: 26.11.2015, 14:00-15:00

    Room: B6 A302

     

    12.11 Discrete Beckner Inequalities via a Bochner-Bakry-Emery Method for Markov Chains (Wen Yue)

    Title of talk: Discrete Beckner Inequalities via a Bochner-Bakry-Emery Method for Markov Chains
    Speaker: Wen Yue (TU Wien)
    Abstract: Beckner inequalities, which interpolate between the logarithmic Sobolev Inequalities and Poincare inequalities, are derived in the context of Markov chains. The proof is based on the Bakry-Emery method and the use of discrete Bochner-type inequalities. We apply our result to several Markov chains including Birth-Death process, Zero-Range process, Bernoulli-Laplace models and Random Transposition models and thus get the exponential convergence rates of the ''distributions'' of these Markov chains to their invariant measures.

    Time: 12.11.2015, 14:00-15:00

    Room: B6 A302

     

    02.11 Derivation of the Vlasov Equation (P. Pickl)

    Title: Derivation of the Vlasov Equation
    Speaker: Peter Pickl (LMU)
    Time: 02.11.2015, 9:30-10:30

    Room: TBA

     

    29.10 On the diffusion limit of the Boltzmann system for gaseous mixtures (F. Salvarani)

    Title: On the diffusion limit of the Boltzmann system for gaseous mixtures.
    Speaker: Francesco Salvarani (University of Pavia, Italy and Université Paris-Dauphine, France)
    Abstract: In this talk, we consider the non-reactive elastic Boltzmann equation for monatomic gaseous mixtures, and we analyse its behaviour under the standard di ffusive scaling. In particular, we point out the relations­hips between the cross sections of the model and the diffusion coefficients, emphasizing the differences with respect to the mono-species case.

    Time: 29.10.2015, 14:00-15:00

    Room: B6 A302

     

    17.09 Finite time versus infinite time blowup for a fully parabolic Keller-Segel system (C. Stinner)

    Title: Finite time versus infinite time blowup for a fully parabolic Keller-Segel system
    Speaker: Christian Stinner (TU Kaiserslautern)
    Abstract: Several variants of the Keller-Segel model are used in mathematical biology to describe the evolution of cell populations due to both diffusion and chemotactic movement. In particular, the emergence of cell aggregation is related to blowup of the solution. Critical nonlinearities with respect to the occurrence of blowup had been identified for a quasilinear parabolic-parabolic Keller-Segel system, but it was not known whether the solution blows up in finite or infinite time. We show that indeed both blowup types appear and that the growth of the chemotactic sensitivity function is essential to distinguish between them. We provide conditions for the existence of each blowup type and discuss their optimality. An important ingredient of our proof is a detailed analysis of the Liapunov functional. This is a joint work with T. Cie´slak (Warsaw).

    Time: 17.09.2015, 14:00-15:00

    Room: B6 A302

     

    14.09 Effective one particle equations I (H. Siedentop)

    Title: Effective one particle equations I
    Speaker: Heinz Siedentop (LMU)
    Time: 14.09.2015, 9:30-11:00

    Room: A5 C116

     

    21.07 Hypocoercivity for a linearized multi-species Boltzmann system (Esther Daus)

    Title: Hypocoercivity for a linearized multi-species Boltzmann system
    Speaker: Esther Daus (TU Wien)
    Abstract: A new coercivity estimate on the spectral gap of the linearized Boltzmann collision operator for multiple species is proved. The assumptions on the collision kernels include hard and Maxwellian potentials under Grad's angular cut-off condition. Two proofs are given: a non-constructive one, based on the decomposition of the collision operator into a compact and a coercive part, and a constructive one, which exploits the ``cross-effects'' coming from collisions between different species and which yields explicit constants. Furthermore, the essential spectra of the linearized collision operator and the linearized Boltzmann operator are calculated. Based on the spectral-gap estimate, the exponential convergence towards global equilibrium with explicit rate is shown for solutions to the linearized multi-species Boltzmann system onthe torus. The convergence is achieved by the interplay between the dissipative collision operator and the conservative transport operator and is proved by using the hypocoercivity method of Mouhot and Neumann.
     

    Time: 21.07.2015, 14:00-15:00

    Room: C012

     

    09.06 Relaxation für parabolische Systeme gemischter Ordnung (Michael Dreher)

    Title: Relaxation für parabolische Systeme gemischter Ordnung
    Speaker: Michael Dreher (Heriot-Watt University Edinburgh)
    Abstract: Motiviert durch numerische Verfahren betrachten wir die Approximation von parabolischen Problemen gemischter Ordnung, wie sie zum Beispiel bei der Beschreibung von fluiddynamischen Systemen mit Kapillaritäts- oder Quanteneffekten auftreten, durch relaxierte Systeme einheitlicher Ordnung.

    Time: 09.06.2015, 14:00-15:00

    Room: B143

     

    05.05 Blowup mechanism of 2D Smoluchowski-Poisson equation: in infinite time quantization and finite time simplicity (Suzuki)

    Title: Blowup mechanism of 2D Smoluchowski-Poisson equation: in infinite time quantization and finite time simplicity
    Speaker: T. Suzuki (Osaka)
    Abstract: The Smoluchowski-Poisson equation was formulated by Sire and Chavanis in the study of Brownian particles, where the variational structure matches the scaling invariance. We show that the blowup in infinite time occurs only when the initial total mass is so quantized as 8\pi times integer. Thus we meet the quantized blowup mechanism of this model in three phases; stationary, finite time, and infinite time. From the argument, simplicity of the collapse formed in finite time is proven. The Kantorovich-Rubinstein metric takes a role in accordance with the improved Trudinger-Moser inequality.

    Time: 05.05.2015, 14:00-15:00

    Room: C116

     

    25.03 Low-dimensional structures of stochastic partial Adaptive methods for exploring differential equations (Z. Zhang)

    Title: Low-dimensional structures of stochastic partial Adaptive methods for exploring differential equations
    Speaker: Zhiwen Zhang (UCLA)

    Time: 25.03.2015  14:00-15:00

    Room: B139

  • 2014

    28.11 Mannheim Half Day Workshop on Analysis

    The main topic of this mini-workshop is on the analysis of diffusion type (reaction diffusion, cross diffusion, diffusion fluid coupled) systems. In the last decades, there are quite a lot of new diffusion type models proposed from biology, which cannot be handled by classical parabolic theory. These have attracted more and more applied mathematicians to generate new tools. The aim of this workshop is to show the new trend of this area and to encourage cooperation on common interested problems. 

    Schedule:

    1:30-2:20  Ansgar Juengel (TU Wien)
    2:20-3:10  Klemens Fellner (University Graz)
    3:10-3:50  Coffee break
    3:50-4:40  Laurent Desvillettes  (CNRS, Paris)
    4:40-5:30  Michael Winkler (University Paderborn)

    Room:  A5,6  012

    Speaker: Ansgar Juengel
    Title:The boundedness-by-entropy principle for cross-diffusion systems from biology
    Abstract: Many systems of collective behavior for multiple species can be described in the continuum limit by cross-diffusion systems, derived e.g. from lattice models. Examples are coming from population dynamics, cell biology, and gas dynamics. A common feature of these strongly coupled parabolic differential equations is that the diffusion matrix is often neither symmetric nor positive definite, which makes the mathematical analysis very challenging.In this talk,we explain that for certain cross-diffusion systems, these difficulties can be overcome by exploiting a formal gradient-flow structure. This means that there exists a transformation of variables (called entropy variables) such that the transformed diffusion matrix becomes positive definite, and there exists a Lyapunov functional (called entropy) which enables suitable a priori estimates. Although the maximum principle generally does not hold for systems, we show that the entropy concept helps to prove lower and upper bounds for the solutions to certain systems, without the use of a maximum principle. We refer to this technique as the boundedness-by-entropy principle. We detail the theory for several examples coming from tumor-growth modeling, population dynamics, and multicomponent gas dynamics. The existence of global weak solutions and their long-time behavior is investigated and some numerical examples are presented.

    Speaker: Klemens Fellner
    Title: On Systems of Reaction-Diffusion Equations: Global Existence and Large Time Analysis.
    Abstract: Starting with a volume-surface reaction-diffusion modelling asymmetric protein localisation on stem cells, we shall discuss questions of global existence, regularity and convergence to equilibrium for systems of reaction-diffusion equations. In particular, we shall present recents results on entropy and duality methods and how they apply to the existence theory and the large time analysis of systems of reaction-diffusion equations. Moreover, we shall point out recent considerations concerning the availability of entropy functional in the case of so-called complex reaction kinetics, where no detailed balance condition holds. 

    Speaker: Laurent Desvillettes
    Title: Some new results for cross diffusion equations
    Abstract: We present recent progresses on the cross diffusion systems first introduced by Shigesada, Teramoto and Kawasaki in the late seventies, obtained in collaboration with Thomas Lepoutre, Ayman Moussa and Ariane Trescases. These improvements include a new analysis of the entropy structure of the system, and new ideas for the approximation of the system.

    Speaker: Michael Winkler
    Title: Mathematical challenges arising in the analysis of chemotaxis-fluid interaction
    Abstract: We consider models for the spatio-temporal evolution of populations of microorganisms, moving in an incopressible fluid, which are able to partially orient their motion along gradients of a chemical signal. According to modeling approaches accounting for the mutual interaction of the swimming cells and the surrounding fluid, we study study parabolic chemotaxis systems coupled to the (Navier-)Stokes equations through transport and buoyancy-induced forces. The presentation discusses mathematical challenges enco­untered even in the context of basic issues such as questions concerning global existence and boundedness, and attempts to illustrate this by reviewing some recent developments. A particular focus will be on strategies toward achieving priori estimates which provide information sufficient not only for the construction of solutions, but also for some qualitative analysis.

     

    27.11 Self-organized Hydrodynamics in an Annular Domain: Modal Analysis and Nonlinear Effects (Hui Yu)

    Title: Self-organized Hydrodynamics in an Annular Domain: Modal Analysis and Nonlinear Effects
    Speaker: Hui Yu (Imperial College)
    Abstract: The Self-Organized Hydrodynamics model of collective behavior is studied on an annular domain. A modal analysis of the linearized model around a perfectly polarized steady-state is conducted. It shows that the model has only pure imaginary modes in countable number and is hence stable. Numerical computations of the low-order modes are provided. The fully non-linear model is numerically solved and nonlinear mode-coupling is then analyzed. Finally, the efficiency of the modal decomposition to analyze the complex features of the nonlinear model is demonstrated.

    Time: 27.11 Do. 15:30

    Place:  B6 A301

     

    20.10 Local existence of smooth solutions to an nonsymmetric hyperbolic system-continued (Jing Wang)

    Title: Local existence of smooth solutions to an nonsymmetric hyperbolic system (Continued)
    Speaker: Jing Wang

    Time: 20.10.2014, Mo. 11:00

    Place: A5 B139

     

    16.10 Local existence of smooth solutions to an nonsymmetric hyperbolic system (Jing Wang)

    Title: Local existence of smooth solutions to an nonsymmetric hyperbolic system
    Speaker: Jing Wang 

    Time: 16.10.2014, Do. 15:00

    Place: A5 B139

     

    30.09, Existence and Blow-Up of Some Parabolic Problems/ Lotka-Volterra Dynamics, (Evangelos Latos)

    Title: Existence and Blow-up of some parabolic problems/ Lotka-Volterra Dynamics
    Speaker: Evangelos Latos
    Abstract: The local existence and uniqueness  of solutions $u=u(x,t;\lambda)$ to the semilinear filtration equation, with initial data $u_0\geq0$ and  appropriate boundary conditions are examined.  There is a critical value $\lambda^*$ of the parameter $\lambda$ such that for $\lambda>\lambda^*$ there is not any kind of stationary solution of the problem, while for $\lambda\leq\lambda^*$ there exist classical stationary solutions. It is proved that the solution $u$, for $\lambda>\lambda^*$, blows-up in finite time $t^*$ for any $u_0\geq0$. 

    A non-local Filtration equation is considered, with some boundary and initial data $u_0$. It is proved that solutions blow-up for large enough values of the parameter $\lambda>0$ and for any $u_0>0$, or for large enough values of $u_0>0$ and for any $\lambda>0$. We will prove the  global grow-up of critical solutions $u^*=u(x,t;\lambda^*)$ ($u^*(x,t)\rightarrow\infty$, as $t\rightarrow\infty$ for all $x\in(-1,1)$).

    A prey-predator system associated with the classical Lotka-Volterra nonlinearity is studied. It is shown that the dynamics of the system are controlled by the ODE part. First the solution becomes spatially homogeneous and is subject to the ODE part as $t\to\infty$. Next  the shadow system  approximates the original system as $D\to\infty$. The asymptotics of the shadow system are also controlled by those of the ODE. The transient dynamics of the original system approaches to the dynamics of its ODE part with the initial mean as $D\to\infty$.

    Time: 30.09, Di. 13:45

    Place: A5 C012

     

    08.05, Lifschitz tails on the Bethe lattice (Francisco Hoecker-Escuti)

    Title: Lifschitz tails on the Bethe lattice
    Speaker: Francisco Hoecker-Escuti
    Abstract: It is well known that the integrated density of states (the normalized eigenvalue counting function) of models of disordered media exhibits an exponential decay near the band edges. This phenomenon is known as Lifschitz tails and it is a hallmark of Anderson localization (the absence of diffusion of waves). In this talk we will discuss the decay of the integrated density of states of the Anderson model whose underlying physical space is a Bethe lattice (the Cayley graph of the free group).

    Time: 08.05, 2pm

    Place: A5 B139

     

    08.04 Die Csisz{\'a}r--Kullback--Ungleichung und Anwendungen (Michael Dreher)

    Titel: Die Csisz{\'a}r--Kullback--Ungleichung und Anwendungen
    Speaker: Michael Dreher (UK)
    Abstrakt: Die Csisz{\'a}r--Kullback--Ungleichung entstammt aus der Wahrscheinlichkeits­theorie bzw. der Informations­theorie und erlaubt es, aus einem Entropiema"s weitere Aussagen „uber die Verteilungs­funktion zu gewinnen. Der Vortrag stellt diese Ungleichung vor und diskutiert Anwendungen auf station"are Probleme aus der Halbleiterphysik.

    Time: 08.04, 2pm

    Place: B6 A302.

     

    02.04, Derivation of Mean-field Dynamics for Fermions (Soeren Petrat)

    Title: Derivation of Mean- field Dynamics for Fermions
    Speaker:  Soeren Petrat (LMU)
    Abstract: The talk is about the derivation of the time-dependent Hartree(-Fock) equations as an e ective dynamics for fermionic many-particle systems in quantum mechanics. That is, I start from the microscopic Schrodinger dynamics for N particles and show that the Hartree(-Fock) equations approximate this dynamics well for large N. I concentrate on the natural scenario where the total kinetic energy is bounded by a constant times N and the interaction has long range, such that there is interesting quantum mechanical mean- fi eld behavior. The main results hold for a large class of interactions, including singular interactions. For Coulomb interaction, the results hold under certain assumptions on the properties of the solutions. The results are obtained by using a new method to derive mean- field limits developed by Pickl, which focuses on the correlations that develop due to the interaction.

    Time: 02.04, 3.30pm

    Place: A5C115

     

    26.03 A note on Aubin-Lions-Dubinskii lemmas (Xiuqing Chen, Peking)

    Title: A note on Aubin-Lions-Dubinskii lemmas
    Speaker: Xiuqing Chen (Peking)
    Abstract: Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinskii lemma are proven, refining some recent results in the literature. The first theorem sharpens slightly a result of Dubinski\u{\i} (1965) for seminormed cones. The second theorem applies to piecewise constant functions in time and sharpens slightly the results of Dreher and Juengel (2012) and Chen and Liu (2012). An application is given, which is useful in the study of porous-medium or fast-diffusion type equations. This is a joint work with Juengel (Wien) and Liu (Duke)

    Time: 26.03, 2pm

    Place: A5 C115

     

    18.02, Mean-field evolution of fermionic systems (Niels Benedikter)

    Title: Mean-field evolution of fermionic systems
    Speaker: Niels Benedikter (Bonn)
    Abstract: Physical systems typically consist of a large number of interacting particles, making it difficult to predict measurements from the time-dependent Schroedinger equation. Therefore one is interested in deriving effective evolution equations approximating the Schroedinger equation. We consider the mean-field regime (high density and weak interaction) for fermionic systems and derive the time-dependent Hartree-Fock equations. We point out a semiclassical structure in typical initial data which is crucial for controlling the approximation up to arbitrary times. (Based on joint work with Marcello Porta and Benjamin Schlein.)

    Time: 18.02, 2pm

    Place: B6  A104