Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 210, pp. 1-22.
Title: Homogenization of a system of semilinear diffusion-reaction
equations in an $H^{1,p}$ setting
Authors: Hari Shankar Mahato (Univ. of Bremen, Bremen, Germany)
Michael Bohm (Univ. of Bremen, Bremen, Germany)
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.