Global existence of solutions in invariant regions for reaction-diffusion systems with a balance law and a full matrix of diffusion coefficients

S. Kouachi, Central University of Tebessa, Algeria

E. J. Qualitative Theory of Diff. Equ., No. 4. (2003), pp. 1-10.

Abstract: In this paper we generalize a result obtained in [15] concerning uniform boundedness and so global existence of solutions for reaction-diffusion systems with a general full matrix of diffusion coefficients satisfying a balance law. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinearity of the reaction term which we take positive in an invariant region has been supposed to be polynomial or of weak exponential growth.

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