GLOBAL EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SYSTEM OF SEMILINEAR DIFFUSION-REACTION EQUATIONS

Abstract

In this paper, we consider a system of highly nonlinear multispecies diffusion-reaction equations with homogeneous Neumann boundary condition. All reactions are reversible (see (1.1)). For this system, the existence and uniqueness of the weak solution are proved on the interval [0; T) for any T > 0. We obtain, global in time, L∞-estimates of the solution with the help of a Lyapunov functional. For the existence of the solution, we use Schaefer’s fixed point theorem, maximal regularity and Lyapunov type arguments.