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Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: Upscaling and corrector estimates for perforated domains
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Eindhoven University of Technology, The Netherlands.
Eindhoven University of Technology, The Netherlands.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
2019 (English)In: Mathematics in Engineering, ISSN 2640-3501, Vol. 1, no 3, p. 548-582Article in journal (Refereed) Published
Abstract [en]

We determine corrector estimates quantifying the convergence speed of the upscaling of a pseudo-parabolic system containing drift terms incorporating the separation of length scales with relative size 1. To achieve this goal, we exploit a natural spatial-temporal decomposition, which splits the pseudo-parabolic system into an elliptic partial differential equation and an ordinary differential equation coupled together. We obtain upscaled model equations, explicit formulas for effective transport coefficients, as well as corrector estimates delimitating the quality of the upscaling. Finally, for special cases we show convergence speeds for global times, i.e., t ∈ R+, by using time intervals expanding to the whole R+ simultaneously with passing to the homogenization limit ↓ 0.

Place, publisher, year, edition, pages
AIMS Press , 2019. Vol. 1, no 3, p. 548-582
Keywords [en]
periodic homogenization, pseudo-parabolic system, mixture theory, upscaled system, corrector estimates, perforated domains
National Category
Mathematics
Research subject
Mathematics; Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-72258DOI: 10.3934/mine.2019.3.548OAI: oai:DiVA.org:kau-72258DiVA, id: diva2:1319819
Available from: 2019-06-03 Created: 2019-06-03 Last updated: 2019-08-28Bibliographically approved

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Vromans, Arthur J.Muntean, Adrian
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CiteExportLink to record
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Citation style
  • apa
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