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A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem
Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för kvalitetsteknik, maskinteknik och matematik.
Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för kvalitetsteknik, maskinteknik och matematik.ORCID-id: 0000-0001-6742-5781
Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för kvalitetsteknik, maskinteknik och matematik.ORCID-id: 0000-0003-2318-1716
Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för kvalitetsteknik, maskinteknik och matematik.
Vise andre og tillknytning
2017 (engelsk)Inngår i: AIP Conference Proceedings / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, artikkel-id UNSP 020177Konferansepaper, Publicerat paper (Fagfellevurdert)
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.

sted, utgiver, år, opplag, sider
American Institute of Physics (AIP), 2017. Vol. 1798, artikkel-id UNSP 020177
Serie
AIP Conference Proceedings, ISSN 0094-243X
HSV kategori
Identifikatorer
URN: urn:nbn:se:miun:diva-30455DOI: 10.1063/1.4972769ISI: 000399203000176Scopus ID: 2-s2.0-85013657168ISBN: 9780735414648 (tryckt)OAI: oai:DiVA.org:miun-30455DiVA, id: diva2:1081147
Konferanse
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
Tilgjengelig fra: 2017-03-13 Laget: 2017-03-13 Sist oppdatert: 2018-12-05bibliografisk kontrollert
Inngår i avhandling
1. Homogenization Results for Parabolic and Hyperbolic-Parabolic Problems and Further Results on Homogenization in Perforated Domains
Åpne denne publikasjonen i ny fane eller vindu >>Homogenization Results for Parabolic and Hyperbolic-Parabolic Problems and Further Results on Homogenization in Perforated Domains
2017 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Sundsvall: Mid Sweden University, 2017. s. 36
Serie
Mid Sweden University licentiate thesis, ISSN 1652-8948 ; 131
HSV kategori
Identifikatorer
urn:nbn:se:miun:diva-30683 (URN)978-91-88527-15-8 (ISBN)
Presentation
2017-05-30, Q221, Akademigatan 1, Östersund, 10:00 (engelsk)
Opponent
Veileder
Merknad

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.

Tilgjengelig fra: 2017-05-03 Laget: 2017-05-02 Sist oppdatert: 2017-05-03bibliografisk kontrollert

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