Autor(en): | Schäffner, Mathias Schweizer, Ben |
Titel: | The time horizon for stochastic homogenization of the one-dimensional wave equation |
Sprache (ISO): | en |
Zusammenfassung: | The wave equation with stochastic coefficients can be classically homogenized on bounded time intervals; solutions converge in the homogenization limit to solutions of a wave equation with constant coefficients. This is no longer true on large time scales: Even in the periodic case with periodicity ε, classical homogenization fails for times of the order ε−2. We consider the one-dimensional wave equation and are interested in the critical time scale ε−β from where on classical homogenization fails. In the general setting, we derive upper and lower bounds for β in terms of the growth rate of correctors. In the specific setting of i.i.d. coefficients with matched impedance, we show that the critical time scale is ε−1 |
Schlagwörter: | wave |
URI: | http://hdl.handle.net/2003/42065 http://dx.doi.org/10.17877/DE290R-23898 |
Erscheinungsdatum: | 2023-07 |
Enthalten in den Sammlungen: | Preprints der Fakultät für Mathematik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
---|---|---|---|---|
StochWavesUpLow-preprint.pdf | DNB | 482.43 kB | Adobe PDF | Öffnen/Anzeigen |
Diese Ressource ist urheberrechtlich geschützt. |
Diese Ressource ist urheberrechtlich geschützt. rightsstatements.org