Heterogeneous Thin Films: Combining Homogenization and Dimension Reduction with Directors
| Autor: | Carolin Kreisbeck, Stefan Krömer |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Characteristic length
Applied Mathematics Dimensionality reduction 010102 general mathematics Locality Mathematical analysis 01 natural sciences Homogenization (chemistry) 010101 applied mathematics Computational Mathematics Quantum nonlocality Mathematics - Analysis of PDEs FOS: Mathematics Relative magnitude 49J45 (primary) 35E99 74K15 74Q05 0101 mathematics Thin film Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | SIAM Journal on Mathematical Analysis. 48:785-820 |
| ISSN: | 1095-7154 0036-1410 |
| DOI: | 10.1137/15m1032557 |
| Popis: | We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness and the period of oscillating microstructures, by means of $\Gamma$-convergence. On a technical level, this requires a subtile merging of homogenization tools, such as multiscale convergence methods, with dimension reduction techniques for functionals subject to differential constraints. One observes that the results depend critically on the relative magnitude between the two scales. Interestingly, this even regards the fundamental question of locality of the limit model, and, in particular, leads to new findings also in the gradient case. Comment: 28 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|