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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 / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, UNSP 020177Conference paper, Published 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, UNSP 020177
Series
AIP Conference Proceedings, ISSN 0094-243X
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-30455DOI: 10.1063/1.4972769ISI: 000399203000176Scopus ID: 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: 2017-06-09Bibliographically approved
In thesis
1. Homogenization Results for Parabolic and Hyperbolic-Parabolic Problems and Further Results on Homogenization in Perforated Domains
Open this publication in new window or tab >>Homogenization Results for Parabolic and Hyperbolic-Parabolic Problems and Further Results on Homogenization in Perforated Domains
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is based on four papers. The main focus is on homogenization of selected parabolic problems with time oscillations, and hyperbolic-parabolic problems without time oscillations. The approaches are prepared by means of certain methods, such as two-scale convergence, multiscale convergence and evolution multiscale convergence. We also discuss further results on homogenization of evolution problems in perforated domains.

Place, publisher, year, edition, pages
Sundsvall: Mid Sweden University, 2017. 36 p.
Series
Mid Sweden University licentiate thesis, ISSN 1652-8948 ; 131
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-30683 (URN)978-91-88527-15-8 (ISBN)
Presentation
2017-05-30, Q221, Akademigatan 1, Östersund, 10:00 (English)
Opponent
Supervisors
Note

Vid tidpunkten för försvar av avhandlingen var följande delarbeten opublicerade: delarbete 1 inskickat, delarbete 2 accepterat, delarbete 4 inskickat.

At the time of the defence the following papers were unpublished: paper 1 submitted, paper 2 accepted, paper 4 submitted.

Available from: 2017-05-03 Created: 2017-05-02 Last updated: 2017-05-03Bibliographically approved

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