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

Raad A.  Obaid; Ghassan A.  Al-Juaifri

doi:10.24996/ijs.2025.66.3.22

Authors

Raad A. Obaid Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa, Kufa, Iraq
Ghassan A. Al-Juaifri Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa, Kufa, Iraq https://orcid.org/0000-0001-5136-3926

DOI:

https://doi.org/10.24996/ijs.2025.66.3.22

Keywords:

Existence, Faedo-Galerkin, Neumann boundary conditions, uniqueness, weak solution, strong solutions, reaction-diffusion, Picard’s Theorem

Abstract

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.