Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: upscaling and corrector estimates for perforated domains

Abstract

In this paper, we determine the convergence speed of an upscaling of a pseudo-parabolic system containing drift terms with scale separation of size $\epsilon \ll 1$. Both the upscaling and convergence speed determination exploit a natural spatial-temporal decomposition, which splits the pseudo-parabolic system into a spatial elliptic partial differential equation and a temporal ordinary differential equation. We extend the applicability to space-time domains that are a product of spatial and temporal domains, such as a time-independent perforated spatial domain. Finally, for special cases we show convergence speeds for global times, i.e. $t\in {\mathbf{R}}_{+}$, by using time intervals that converge to ${\mathbf{R}}_{+}$ as $\epsilon \downarrow 0$.

35 pages, 0 figures

References in corpus (1)

• Existence of weak solutions for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations