Said Kouachi

Invariant Regions and Global Existence of Solutions For Reaction-Diffusion Systems with a Full Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions

Abstract:
The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for reaction-diffusion systems with a general full matrix of diffusion coefficients without balance law'condition ($f+g\equiv 0)$ and with nonhomogeneous boundary conditions. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth.

Keywords:
Reaction diffusion systems, invariant regions, Lyapunov functionals, global existence.

MSC 2000: 35K57, 35K45.