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Volume 3, Number 4, 2013, Pages 357-376                                                                DOI:10.11948/2013027
Global existence and uniqueness for a system of semilinear multi-species diffusion-reaction equations
Hari Shankar Mahato,Michael Bohm
Keywords:Global solution, semilinear parabolic equation, reversible reactions, Lyapunov functionals, maximal regularity
      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.
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