2022/01/07 by Alain Blaustein, Blaustein, Alain, Francis Filbet +1
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Lipid Membrane Structure and Behavior #Mathematical Biology Tumor Growth #Theoretical and Computational Physics #Thermoelastic and Magnetoelastic Phenomena #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2201.02363
openalex publication_date 2022/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider a spatially extended mesoscopic FitzHugh-Nagumo model with strong local interactions and prove that its asymptotic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. As the local interactions strongly dominate, the weak solution to the mesoscopic equation under consideration converges to the local equilibrium, which has the form of Dirac distribution concentrated to an averaged membrane potential. Our approach is based on techniques widely developed in kinetic theory (Wasserstein distance, relative entropy method), where macroscopic quantities of the mesoscopic model are compared with the solution to the nonlocal reaction-diffusion system. This approach allows to make the rigorous link between microscopic and reaction-diffusion models.