LMA - Laboratoire de Mécanique et d’Acoustique

A. Lamacz-Keymling - Waves in heterogeneous media : derivation of dispersive effective models

Amphithéâtre François Canac, LMA

Le 16 novembre 2021 de 11h00 à 12h00

Agnes Lamacz-Keymling / Universität Duisburg-Essen ; Fakultät für Mathematik

Abstract :

We investigate wave propagation in a heterogeneous medium. A disturbance (the deformation in an elastic wave or the magnetic field in an electro-magnetic wave) is described by a second order wave equation in divergence form,

We assume that the coefficient is of the form

such that the medium has heterogeneities on the small scale "epsilon". According to classical homogenization results from the 1990’ies, on time scales of order 1, the effective properties of the medium are well-described by the effective wave equation

However, when

dispersive effects have to be taken into account. We demonstrate an analysis of the problem and derive a dispersive effective equation that describes u^epsilon on large time scales.

Numerical tests show the effectiveness of the limit system in one- and two-dimensional examples.

This is joint work with G. Allaire, T. Dohnal, J. Rauch and B. Schweizer.

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