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Homogenization of linear parabolic equations with a certain resonant matching between rapid spatial and temporal oscillations in periodically perforated domains
Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
2019 (English)In: Acta Mathematicae Applicatae Sinica (English Series), ISSN 0168-9673, E-ISSN 1618-3932, Vol. 35, no 2, p. 340-358Article in journal (Refereed) Published
Abstract [en]

In this article, we study homogenization of a parabolic linear problem governed by a coefficient matrix with rapid spatial and temporal oscillations in periodically perforated domains with homogeneous Neumann data on the boundary of the holes. We prove results adapted to the problem for a characterization of multiscale limits for gradients and very weak multiscale convergence.

Place, publisher, year, edition, pages
2019. Vol. 35, no 2, p. 340-358
Keywords [en]
Homogenization, two-scale convergence, multiscale convergence, periodically perforated domains ack, norm approximation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-30695DOI: 10.1007/s10255-019-0810-1ISI: 000467899800008Scopus ID: 2-s2.0-85065704100OAI: oai:DiVA.org:miun-30695DiVA, id: diva2:1092433
Available from: 2017-05-02 Created: 2017-05-02 Last updated: 2019-11-20Bibliographically 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
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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Lobkova, Tatiana

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