Electron. J. Diff. Equ., Vol. 2015 (2015), No. 94, pp. 1-11.

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

Safia Henine, Salem Abdelmalek, Amar Youkana

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.

Submitted January 8, 2015. Published April 14, 2015.
Math Subject Classifications: 35K57.
Key Words: Gierer-Meinhardt system; Lyapunov functional; Uniform boundedness.

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  Safia Henine
Department of Mathematics
University of Batna 05000, Algeria
email: henine.safia@yahoo.fr
Salem Abdelmalek
Department of Mathematics, College of Sciences
Yanbu Taibah University, Saudi Arabia.
email: sabdelmalek@taibahu.edu.sa
  Amar Youkana
Department of Mathematics
University of Batna 05000, Algeria
email: youkana_amar@yahoo.fr

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