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

Arthur Vromans, Fons van de Ven, A. Muntean (Corresponding author)

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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 ϵ≪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∈R+, by using time intervals that converge to R+ as ϵ↓0.
Translated title of the contributionHomogenizatie van een pseudo-parabolisch systeem via een spatiaal-temporale ontkoppeling: opschaling en corrector schattingen voor geperforeerde domeinen
Original languageEnglish
Pages (from-to)548–582
Number of pages35
JournalMathematics in Engineering
Volume1
Issue number3
DOIs
Publication statusPublished - 12 Jul 2019

Keywords

  • Corrector estimates
  • Mixture theory
  • Perforated domains
  • Periodic homogenization
  • Pseudo-parabolic system
  • Upscaled system

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