Joint French-Czech mathematics meeting

INSA-Lyon, November 29-30, 2018

Francis Filbet

Université de Toulouse III

Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system

We introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. Our approach is based on a relative entropy method, where the macroscopic quantities of the kinetic model are compared with the solution to the nonlocal reaction-diffusion system. This approach allows to make the rigorous link between kinetic and reaction-diffusion models.