On the interplay of two-scale convergence and translation
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Contributors
Abstract
We study the effects of translation on two-scale convergence. Given a two-scale convergent sequence (u epsilon(x))epsilon with two-scale limit u(x, y), then in general the translated sequence (u epsilon(x + t))epsilon is no longer two-scale convergent, even though it remains two-scale convergent along suitable subsequences. We prove that any two-scale cluster point of the translated sequence is a translation of the original limit and has the form u(x + t,y + r) where the microscopic translation r belongs to a set that is determined solely by t and the vanishing sequence (epsilon). Finally, we apply this result to a novel homogenization problem that involves two different coordinate frames and yields a limiting behavior governed by emerging microscopic translations.
Details
Original language | English |
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Pages (from-to) | 163-183 |
Number of pages | 21 |
Journal | Asymptotic Analysis |
Volume | 71 |
Issue number | 3 |
Publication status | Published - 2011 |
Peer-reviewed | Yes |
Externally published | Yes |
External IDs
Scopus | 79952797799 |
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Keywords
Keywords
- two-scale convergence, translation, homogenization, Gamma-convergence, BLOCH-WAVE HOMOGENIZATION, DOUBLE-POROSITY MODEL, INTEGRAL FUNCTIONALS, ASYMPTOTIC ANALYSIS, FLOW