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.
Reaction diffusion systems, invariant regions, Lyapunov functionals, global existence.
MSC 2000: 35K57, 35K45.