A spectral ansatz for the long-time homogenization of the wave equation
- Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present work is a new ansatz for the long-time two-scale expansion inspired by spectral analysis. Based on this spectral ansatz, we extend and refine all previous results in the field, proving homogenization up to optimal timescales with optimal error estimates, and covering all the standard assumptions on heterogeneities (both periodic and stationary random settings).
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| Author: | Mitia Duerinckx, Antoine Gloria, Matthias RufGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1137324 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/113732 |
| ISSN: | 2270-518XOPAC |
| Parent Title (French): | Journal de l'École polytechnique — Mathématiques |
| Publisher: | Cellule MathDoc/Centre Mersenne |
| Place of publication: | Paris |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2024/07/01 |
| Volume: | 11 |
| First Page: | 523 |
| Last Page: | 587 |
| DOI: | https://doi.org/10.5802/jep.259 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
