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Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system Filbet, Francis

Description

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 rigourous link between kinetic and reaction-diffusion models

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