Electron. J. Diff. Equ., Vol. 2012 (2012), No. 55, pp. 1-8.

Existence of global solutions for a Gierer-Meinhardt system with three equations

Salem Abdelmalek, Hichem Louafi, Amar Youkana

This articles shows the existence of global solutions for a Gierer-Meinhardt model of three substances described by reaction-diffusion equations with fractional reactions. Our technique is based on a suitable Lyapunov functional.

Submitted March 22, 2012. Published April 5, 2012.
Math Subject Classifications: 35K57, 92C15.
Key Words: Gierer-Meinhardt system; Lyapunov functional; activator-inhibitor.

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Salem Abdelmalek
Department of Mathematics, College of Arts and Sciences
Yanbu Taibah University, Saudi Arabia.
email: sallllm@gmail.com
  Hichem Louafi
Faculty of Economics and Management Science
University of Batna, 5000 Algeria
email: hichemlouafi@gmail.com
  Amar Youkana
Department of Mathematics, University of Batna
5000 Algeria
email: youkana_amar@yahoo.fr

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