Boundedness and large-time behavior of solutions for a Gierer-Meinhardt system of three equations

Abstract

The aim of this work is to prove the uniform boundedness and the existence of global solutions for Gierer-Meinhardt model of three substance described by reaction-diffusion equations with Neumann boundary conditions. Based on a Lyapunov functional we establish the asymptotic behaviour of the solutions.

Keywords

• Gierer-Meinhardt system
• Lyapunov functional
• Uniform boundedness