Authors: Lamacz, Agnes
Title: Dispersive effective models for waves in heterogeneous media
Language (ISO): en
Abstract: We study the long time behavior of waves in a strongly heterogeneous medium, starting from the one-dimensional scalar wave equation with variable coefficients. We assume that the coefficients are periodic with period ɛ and ɛ > 0 is a small length parameter. Our main result is the rigorous derivation of two different dispersive models. The first is a fourth-order equation with constant coefficients including powers of ɛ . In the second model, the ɛ-dependence is completely avoided by considering a third-order linearized Korteweg-de-Vries equation. Our result is that both simplified models describe the long time behavior well. An essential tool in our analysis is an adaption operator which modifies smooth functions according to the periodic structure of the medium.
Subject Headings: homogenization
wave equation
dispersive model
long time behavior
Issue Date: 2010-03-23T14:45:40Z
Appears in Collections:Preprints der Fakultät für Mathematik

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