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Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal 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.
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
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper we prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of epsilon. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evolution problems. At the end of the paper an example is given to concretize the use of the main result.

National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-30685OAI: oai:DiVA.org:miun-30685DiVA: diva2:1092384
Available from: 2017-05-02 Created: 2017-05-02 Last updated: 2017-05-03
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

Open Access in DiVA

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Other links

https://arxiv.org/abs/1704.01375

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Flodén, LiselottJonasson, PernillaOlsson Lindberg, MarianneLobkova, Tatiana
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Citation style
  • apa
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