Diffusion limit of a transport equation leading to volume-exclusion chemotaxis

Diane Peurichard (INRIA Paris)

Nov 23. 2022, 10:00 — 10:45

In this talk, we investigate the diffusion limit of a kinetic 'velocity-jump' model where both the transport term and the turning operator are density dependent, leading to volume-exclusion chemotactic equations. We then numerically investigate whether the relevant macroscopic volume-exclusion equation corresponds to the underlying physical system described by the kinetic equation in the diffusion limit, by means of a generalized asymptotic preserving scheme based on a micro-macro decomposition. The scheme produces accurate approximations also in the case of strong chemosensitivity. We extend this scheme to two dimensional kinetic models and we validate its efficiency by means of 1D and 2D numerical experiments of pattern formation in biological systems, giving insights into how the individual mechanisms at the cell level can lead to volume-exclusion effects at the population level. 

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Mathematical Methods for the Study of Self-organization in the Biological Sciences (Thematic Programme)
Pierre Degond (IMT)
Marie Doumic (Sorbonne U, Paris)
Anna Kicheva (ISTA, Klosterneuburg)
Sara Merino-Aceituno (U of Vienna)
Christian Schmeiser (U of Vienna)