1. The time horizon for stochastic homogenization of the one-dimensional wave equation.
- Author
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Schäffner, M. and Schweizer, B.
- Subjects
- *
TIME perspective , *ASYMPTOTIC homogenization , *WAVE equation - 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 scaleε 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 forβ 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 . [ABSTRACT FROM AUTHOR]- Published
- 2024
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