Global existence of solutions for Gierer-Meinhardt system with three equations

TL;DR

This paper proves the global existence of solutions for a three-equation Gierer-Meinhardt reaction-diffusion system with fractional reactions using Lyapunov functionals, addressing boundedness challenges.

Contribution

It introduces a novel approach employing Lyapunov functionals to establish global solutions for a fractional Gierer-Meinhardt system.

Findings

Established global existence of solutions for the system.

Developed a Lyapunov functional method for fractional reaction-diffusion systems.

Addressed boundedness issues in fractional terms.

Abstract

This paper deals with an Gierer-Meinhardt model, with three substances, formed Reaction-Diffusion system with fractional reaction. To prove global existence for solutions of this system presents difficulties at the boundednees of fractionar term. The purpose of this paper is to prove the existence of a global solution using a boundary functionel. Our technique is based on the construction of Lyapunov functionel.