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G-Convergence and Homogenization of some Monotone Operators
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.ORCID iD: 0000-0003-2942-6841
2008 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

In this thesis we investigate some partial differential equations with respect to G-convergence and homogenization. We study a few monotone parabolic equations that contain periodic oscillations on several scales, and also some linear elliptic and parabolic problems where there are no periodicity assumptions. To begin with, we examine parabolic equations with multiple scales regarding the existence and uniqueness of the solution, in view of the properties of some monotone operators. We then consider G-convergence for elliptic and parabolic operators and recall some results that guarantee the existence of a well-posed limit problem. Then we proceed with some classical homogenization techniques that allow an explicit characterization of the limit operator in periodic cases. In this context, we prove G-convergence and homogenization results for a monotone parabolic problem with oscillations on two scales in the space variable. Then we consider two-scale convergence and the homogenization method based on this notion, and also its generalization to multiple scales. This is further extended to the case that allows oscillations in space as well as in time. We prove homogenization results for a monotone parabolic problem with oscillations on two spatial scales and one temporal scale, and for a linear parabolic problem where oscillations occur on one scale in space and two scales in time. Finally, we study some linear elliptic and parabolic problems where no periodicity assumptions are made and where the coefficients are created by certain integral operators. Here we prove results concerning when the G-limit may be obtained immediately and is equal to a certain weak limit of the sequence of coefficients.

Place, publisher, year, edition, pages
Östersund: Mid Sweden Univ , 2008. , p. 141
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 45
Keyword [en]
G-convergence, homogenization, two-scale convergence
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-94ISBN: 978-91-85317-85-1 (print)OAI: oai:DiVA.org:miun-94DiVA, id: diva2:1655
Public defence
2008-02-28, Q221, Q, Akademigatan 1, Östersund, 13:00 (English)
Opponent
Supervisors
Available from: 2008-02-10 Created: 2008-02-10 Last updated: 2013-11-01Bibliographically approved

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Olsson, Marianne

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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf