Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions

S. Kouachi, Central University of Tebessa, Algeria

E. J. Qualitative Theory of Diff. Equ., No. 2. (2002), pp. 1-10.

Abstract: In this article, we generalize the results obtained in [16] concerning uniform bounds and so global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients satisfying a balance law and with homogeneous Neumann boundary conditions. Our techniques are based on invariant regions and Lyapunov functional methods. We demonstrate that our results remain valid for nonhomogeneous boundary conditions and with out balance law's condition. The nonlinear reaction term has been supposed to be of polynomial growth.

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