Existence globale pour des systèmes de réaction-diffusion avec contrôle de masse

Abstract

This work is a contribution to the study of global existence in time of solutions for reaction-diffusion systems where the structure of the nonlinear terms a priori implies that the total mass of the solution is uniformly bounded. This type of systems often appears in applications. Our first contribution is devoted to the study of global existence and asymptotic behavior of solutions for reaction-diffusion systems with nonlinearities of exponential growth (or faster). For this purpose, we use the appropriate techniques which are based on semigroups, energy estimates and Lyapunov functional methods. In the second part of this work, we are interested in the study of global existence in time for reaction-diffusion systems with a tridiagonal matrix of diffusion coefficients. For this end, we construct the invariant regions in which we can demonstrate that for any initial data in this regions, the problem considered is equivalent to a problem for which the global existence follows by a usual technique based on Lyapunov functional.