Said Kouachi and Belgacem Rebiai

Invariant Regions and the Global Existence for Reaction-Diffusion Systems with a Tridiagonal Matrix of Diffusion Coefficients

abstract:
The aim of this study is to prove the global existence of solutions for reaction-diffusion systems with a tridiagonal matrix of diffusion coefficients and nonhomogeneous boundary conditions. In so doing, we make use of the
appropriate techniques which are based on invariant domains and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth. This result is a continuation of that by Kouachi (2004).

Mathematics Subject Classification: 35K45, 35K57

Key words and phrases: Reaction diffusion systems, invariant domains, Lyapunov functionals, global existence