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Article type: Research Article
Authors: Schäffner, M.a | Schweizer, B.b; *
Affiliations: [a] Institut für Mathematik, MLU Halle-Wittenberg, Theodor-Lieser-Straße 5, 06120 Halle (Saale), Germany | [b] Fakultät für Mathematik, TU Dortmund, Vogelspothsweg 87, 44227 Dortmund, Germany
Correspondence: [*] Corresponding author. E-mail: ben.schweizer@tu-dortmund.de.
Abstract: The wave equation with stochastic rapidly oscillating 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 with random rapidly oscillation coefficients on scale ε 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.
Keywords: Stochastic homogenization, wave equation
DOI: 10.3233/ASY-241923
Journal: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-39, 2024
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