Electron. J. Diff. Equ., Vol. 2013 (2013), No. 210, pp. 1-22.

Homogenization of a system of semilinear diffusion-reaction equations in an $H^{1,p}$ setting

Hari Shankar Mahato, Michael Bohm

Abstract:
In this article, homogenization of a system of semilinear multi-species diffusion-reaction equations is shown. The presence of highly nonlinear reaction rate terms on the right-hand side of the equations make the model difficult to analyze. We obtain some a-priori estimates of the solution which give the strong and two-scale convergences of the solution. We homogenize this system of diffusion-reaction equations by passing to the limit using two-scale convergence.

Submitted July 14, 2013. Published September 19, 2013.
Math Subject Classifications: 35B27, 35K57, 35K58, 46E35, 35D30.
Key Words: Global solution; semilinear parabolic equation; reversible reactions; Lyapunov functionals; maximal regularity; homogenization; two-scale convergence.

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Hari Shankar Mahato
Center of Industrial Mathematics, University of Bremen
D-28359, Bremen, Germany
email: mahato@math.uni-bremen.de
Michael Böhm
Center of Industrial Mathematics, University of Bremen
D-28359, Bremen, Germany
email: mbohm@math.uni-bremen.de

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