Analysis of a nonlinear reaction-diffusion system of the Fitzhugh-Nagumo type with Robin boundary conditions

We analyze the system of reaction-diffusion equations of the Fitzhugh-Nagumo (FHN) type on open bounded convex domains D⊂Rd(d≤3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {D} \subset \mathbb {R}^{d} (d \le 3)$$\end{document} with Robin boundary conditions. The Classical Faedo-Galerkin approach Lions (Quelques méthodes de résolution des problemes aux limites non linéaires 1969) and compactness arguments are utilised to show the existence, uniqueness, and continuous dependence on initial data of weak and strong solutions. Moreover, we introduce a complete case study for the application of this approach to the Fitzhugh-Nagumo system.