The goal of this article is to study the existence of classical solutions global in time for reaction-diffusion systems with strong coupling in the diffusion and with exponential growth (or without any growth) conditions on the nonlinear reactive terms. This extends some similar results in the case of a diagonal diffusion-operator associated with nonlinearities preserving the positivity and the total mass of the solutions or for which the total mass is a priori bounded.
Submitted January 16, 2011. Published August 7, 2011.
Math Subject Classifications: 35K45, 35K57.
Key Words: Reaction-diffusion systems; Lyapunov functional; global solution.
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| Belgacem Rebiai |
Department of Mathematics and Informatics
Tebessa University 12002, Algeria
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