Belgacem Rebiai

Invariant Domains and 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. Towards this end, we make use of the appropriate techniques which are based on the invariant domains and on Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth. This result is a continuation of that due to Kouachi and Rebiai [Invariant regions and the global existence for reaction-diffusion systems with a tridiagonal matrix of diffusion coefficients. Mem. Differential Equations Math. Phys. 51 (2010), 93-108.

Mathematics Subject Classification: 35K45, 35K57

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