Homogenization of a diffusion‐reaction system with surface exchange and evolving hypersurface
S. Dobberschütz · Mathematical Methods in the Applied Sciences · 2014
This paper is concerned with the homogenization of a diffusion‐reaction process in a domain undergoing an evolution of the microstructure. The main novelty is the consideration of a chemical process on a hypersurface, where the surface itself is evolving. After transformation to a description in a fixed domain, we employ methods of periodic homogenization to arrive at a limit problem in the bulk coupled with problems in a reference cell. Here, the structural evolution takes place only in the reference structure. Additional problems come from nonlinear reaction rates, which require the Kolmogoroff compactness criterion for the derivation of suitablea prioriestimates. The results can be used as a modeling tool and for the investigation of complex biological and chemical systems in porous media, for example, carbon sequestration or biological enhanced oil recovery. Copyright © 2014 John Wiley & Sons, Ltd.