On the interplay of two-scale convergence and translation
Research output: Contribution to journal › Research article › Contributed › peer-review
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.
|Number of pages||21|
|Publication status||Published - 2011|
- two-scale convergence, translation, homogenization, Gamma-convergence, BLOCH-WAVE HOMOGENIZATION, DOUBLE-POROSITY MODEL, INTEGRAL FUNCTIONALS, ASYMPTOTIC ANALYSIS, FLOW