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Homogenization of Some Selected Elliptic and Parabolic Problems Employing Suitable Generalized Modes of Two-Scale Convergence
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.ORCID iD: 0000-0001-9984-2424
2010 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. Concerning the multiscaled parabolic problems, we find that the result of the homogenization depends on the behavior of the temporal scale functions. The temporal scale functions considered in the thesis may, in the sense explained in the text, be slow or rapid and in resonance or not in resonance with respect to the spatial scale function. The homogenization for the possibly non-periodic elliptic problems gives the same result as for the corresponding periodic problems but with the exception that the local gradient operator is everywhere substituted by a differential operator consisting of a product of the local gradient operator and matrix describing the geometry and which depends, effectively, parametrically on the global variable.

Place, publisher, year, edition, pages
Östersund: Mittuniversitetet , 2010. , p. viii + 124
Series
Mid Sweden University licentiate thesis, ISSN 1652-8948 ; 45
Keyword [en]
H-convergence, G-convergence, homogenization, multiscale analysis, two-scale convergence, multiscale convergence, elliptic partial differential equations, parabolic partial differential equations, monotone operators, heterogeneous media, non-periodic media
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:miun:diva-11991ISBN: 978-91-86073-90-9 (print)OAI: oai:DiVA.org:miun-11991DiVA, id: diva2:352294
Presentation
2010-10-06, Q221, Hus Q, Akademigatan 1, Östersund, 13:00 (Swedish)
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Available from: 2010-09-20 Created: 2010-09-20 Last updated: 2013-11-01Bibliographically approved

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Persson, Jens

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CiteExportLink to record
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Citation style
  • apa
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  • Other style
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Language
  • de-DE
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  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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