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

Hari Shankar Mahato; Michael Böhm

doi:10.11948/2013027

2013 Volume 3 Issue 4

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Hari Shankar Mahato, Michael Böhm. GLOBAL EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SYSTEM OF SEMILINEAR DIFFUSION-REACTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2013, 3(4): 357-376. doi: 10.11948/2013027

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Hari Shankar Mahato, Michael Böhm. GLOBAL EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SYSTEM OF SEMILINEAR DIFFUSION-REACTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2013, 3(4): 357-376. doi: 10.11948/2013027

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

Center of Industrial Mathematics, University of Bremen, Bibliothekstr. 1, 28359 Bremen, Germany

Abstract

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.
- Global solution /
- nonlinear parabolic equation /
- reversible reactions /
- Lyapunov functionals /
- maximal regularity
MSC: 35K57;35K55;76S05;47J35

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