A priori estimates for excitable models

TL;DR

This paper derives existence, uniqueness, and a priori estimates for the Fitzhugh Nagumo reaction-diffusion system using an equivalent integrodifferential equation approach, applicable to various dissipative models.

Contribution

It introduces a novel method of analyzing the Fitzhugh Nagumo system via an equivalent integrodifferential equation, extending results to both linear and nonlinear cases.

Findings

Established existence and uniqueness results.

Derived a priori estimates for solutions.

Unified analysis applicable to multiple dissipative models.

Abstract

The reaction-diffusion system of Fitzhugh Nagumo is considered. The initial- boundary problems with Neumann and Dirichlet conditions are analyzed. By means of an equivalent semilinear integrodifferential equation which characterizes several dissipative models of viscoelasticity, biology, and superconductivity, some results on existence, uniqueness and a priori estimates are deduced both in the linear case and in the non linear one.