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In this paper, we consider a system of highly nonlinear multi- species diffusion-reaction equations with homogeneous Neumann boundary condition. All reactions are reversible (see (1.1)). For this system, the exis- tence 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.

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