Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system
Analysis of PDEs
2018-04-12 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1804.01263,
title = {Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system},
author = {Joachim Crevat and Grégory Faye and Francis Filbet},
journal= {arXiv preprint arXiv:1804.01263},
year = {2018}
}