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Homogenization of a Hyperbolic-Parabolic Problem with Three Spatial Scales
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.ORCID iD: 0000-0003-2318-1716
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.ORCID iD: 0000-0003-2942-6841
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2017 (English)In: Progress in Industrial Mathematics at ECMI 2016 / [ed] Quintela, P., Barral, P., Gómez, D., Pena, F.J., Rodríguez, J., Salgado, P., Vázquez-Mendéz, M.E., Springer, 2017, p. 617-623Conference paper, Published paper (Refereed)
Abstract [en]

We study the homogenization of a certain linear hyperbolic-parabolic problem exhibiting two rapid spatial scales {ε; ε2}. The homogenization is performed by means of evolution multiscale convergence, a generalization of the concept of two-scale convergence to include any number of scales in both space and time. In particular we apply a compactness result for gradients. The outcome of the homogenization procedure is that we obtain a homogenized problem of hyperbolic-parabolic type together with two elliptic local problems, one for each rapid scale, for the correctors.
Place, publisher, year, edition, pages
Springer, 2017. p. 617-623
Series
Mathematics in Industry, ISSN 1612-3956 ; 26
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-30694DOI: 10.1007/978-3-319-63082-3_94ISBN: 978-3-319-63081-6 (print)OAI: oai:DiVA.org:miun-30694DiVA, id: diva2:1092432
Conference
ECMI-16, the 19th European Conference on Mathematics for Industry at Santiago de Compostela, 13-17th June 2016.
Available from: 2017-05-02 Created: 2017-05-02 Last updated: 2020-07-09Bibliographically 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. p. 36
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
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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, LiselottHolmbom, AndersJonasson, PernillaOlsson Lindberg, MarianneLobkova, TatianaPersson, Jens

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