Special Session 83: New Aspects of Mathematical Modeling and Analysis in Materials Science

Homogenization of a Stokes-Reaction System with Evolving Microstructure
Michael Eden
University of Regensburg
Germany
Co-Author(s):    Richard H\{o}fer
Abstract:
We study a coupled Stokes-reaction-diffusion system posed in a non-periodically perforated domain where the size of solid ball inclusions of size $\sim\varepsilon^\alpha$ evolves through a surface reaction mechanism. We consider the scaling regime $\alpha\in(1,3]$ for the size of the inclusions and show local-in-time well-posedness for the micro-problem via a contraction mapping argument. We then analyze the asymptotic behavior $\varepsilon\to0$ as the microstructure size tends to zero. Depending on the scaling parameter $\alpha$, we get different limiting regimes, including a critical case and subcritical regimes