DAAD-PPP Frankreich: Non-local conservation laws for engineering applications

Project Description

This project tackles theoretical and numerical issues arising in the mathematical study of conservation laws with non-local flux functions. These equations appear in a variety of applications, ranging from traffic flows to industrial processes and biology, and are intended to model macroscopically the action of non-local interactions occurring at the microscopic level. Targeted applications include vehicular traffic (mainly in connection with vehicle-to-vehicle communication and consumption/pollution estimation), crowd motion (in connection with safe building evacuation procedures), and manufacturing systems (intelligent production).

Key words: conservation laws, non-local flux functions, analysis and numerical simulation

Project Partners:

Dr. Paola Goatin (INRIA Sophia Antipolis – Méditerranée, Nice, France)
Prof. Dr. Simone Göttlich (University of Mannheim, Germany)

Funding: DAAD within the project “PPP France – PROCOPE 2019/2020”; travel expenses for two years

Duration: 01/2019 – 12/2021

Relevant Publications

• F. Chiarello, J. Friedrich, P. Goatin, S. Göttlich – Micro-Macro limit of a non-local generalized Aw-Rascle type model, SIAM J. Appl. Math., Vol.80(4), pp. 1841-1861, 2020.
• O. Kolb, G. Costeseque, P. Goatin, S. Göttlich – Pareto-optimal coupling conditions for a second order traffic flow model at junctions – SIAM J. Applied Mathematics (SIAP), Vol. 78(4), pp. 1981- 2002, 2018.