Electron. J. Diff. Eqns., Vol. 2001(2001), No. 68, pp. 1-10.

Existence of global solutions to reaction-diffusion systems via a Lyapunov functional

Said Kouachi

The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations) which give Lp-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].

Submitted May 29, 2001. Published October 23, 2001.
Math Subject Classifications: 35K45, 35K57.
Key Words: Reaction-diffusion systems, global existence, Lyapunov functional.

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Said Kouachi
Centre universitaire de Tebessa
departement de mathematiques
12002, Tebessa, Algerie
e-mail: kouachi.said@caramail.com

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