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Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations
University of Bremen.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.ORCID iD: 0000-0002-1160-0007
2017 (English)In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, no 57, 1-21 p.Article in journal (Refereed) Published
Abstract [en]

We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in [11] by two-scale convergence arguments. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing a priori known phase transformations. While such estimates seem not to be obtainable in the fully coupled setting, we show that for some simplified scenarios optimal convergence rates can be proven rigorously. The main technique for the proofs are energy estimates using special reconstructions of two-scale functions and particular operator estimates for periodic functions with zero average. Here, additional regularity results for the involved functions are necessary.

Place, publisher, year, edition, pages
2017. no 57, 1-21 p.
Keyword [en]
Homogenization; two-phase thermoelasticity; corrector estimates; time-dependent domains; distributed microstructures
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-47970OAI: oai:DiVA.org:kau-47970DiVA: diva2:1075336
Available from: 2017-02-17 Created: 2017-02-17 Last updated: 2017-03-28

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http://ejde.math.txstate.edu/Volumes/2017/57/abstr.html

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf