Some remarks on two-scale convergence and periodic unfolding

The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of th...

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Bibliographic Details
Published inApplications of mathematics (Prague) Vol. 57; no. 4; pp. 359 - 375
Main Authors Franců, Jan, Svanstedt, Nils E. M.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.08.2012
Springer Nature B.V
Subjects
Adjoints
Analysis
Applications of Mathematics
Applied mathematics
Classical and Continuum Physics
Convergence
Homogenization
Homogenizing
Integrals
Matematik
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Optimization
Proving
Studies
Theoretical
two-scale convergence
unfolding
homogenization
35B27
unfolding
two-scale convergence
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Summary:The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization to non-periodic homogenization.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0862-7940
1572-9109
1572-9109
DOI:10.1007/s10492-012-0021-z