Existence and Uniqueness of the Solution to the Reaction-Diffusion System of FHN type

In this study, we delve into the intricacies of the reaction-diffusion system associated with neuronal activities, focusing on open bounded three dimensions convex domain. Employing the renowned Faedo-Galerkin method, alongside compactness techniques, we establish the uniqueness, existence, and initial data sensitivity of both weak and strong solutions within this framework. Furthermore, a comprehensive case analysis is presented, demonstrating the practical application of this methodology to the reaction-diffusion system under consideration.