Electron. J. Diff. Eqns., Vol. 2008(2008), No. 141, pp. 1-9.

Existence of global solutions for a system of reaction-diffusion equations having a triangular matrix

El Hachemi Daddiouaissa

Abstract:
We consider the system of reaction-diffusion equations
$$\displaylines{ u_{t}-a\Delta u=\beta-f(u,v)-\alpha u,\cr v_{t}-c\Delta u-d\Delta v=g(u,v)-\sigma v. }$$
Our aim is to establish the existence of global classical solutions using the method used by Melkemi, Mokrane, and Youkana [19].

Submitted August 19, 2007. Published October 16, 2008.
Math Subject Classifications: 35K57, 35K45.
Key Words: Reaction-diffusion systems; Lyapunov functional; global solution.

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El Hachemi Daddiouaissa
Department of Mathematics, University Kasdi Merbah, UKM
Ouargla 30000, Algeria
email: dmhbsdj@gmail.com

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