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A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.ORCID iD: 0000-0001-6742-5781
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
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2017 (English)In: AIP Conference Proceedings, American Institute of Physics (AIP), 2017, Vol. 1798, 020177Conference paper (Refereed)
Abstract [en]

We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ϵ→0. We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ϵ-1∂tuϵ as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2017. Vol. 1798, 020177
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-30455DOI: 10.1063/1.4972769ScopusID: 2-s2.0-85013657168ISBN: 978-073-5414-64-8 (print)OAI: oai:DiVA.org:miun-30455DiVA: diva2:1081147
Conference
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, 4 July 2016 through 8 July 2016, University of La Rochelle La Rochelle; France
Available from: 2017-03-13 Created: 2017-03-13 Last updated: 2017-04-10

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Flodén, LottaHolmbom, AndersJonasson, PernillaLobkova, TatianaOlsson Lindberg, Marianne
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CiteExportLink to record
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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
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  • asciidoc
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