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Annali di Matematica Pura ed Applicata

, 188:561

First Online: 13 September 2008Received: 23 November 2007

Abstract

We study the homogenization and singular perturbation of the wave equation in a periodic media for long times of the order of the inverse of the period. We consider initial data that are Bloch wave packets, i.e., that are the product of a fast oscillating Bloch wave and of a smooth envelope function. We prove that the solution is approximately equal to two waves propagating in opposite directions at a high group velocity with envelope functions which obey a Schrödinger type equation. Our analysis extends the usual WKB approximation by adding a dispersive, or diffractive, effect due to the non uniformity of the group velocity which yields the dispersion tensor of the homogenized Schrödinger equation.

KeywordsHomogenization Bloch waves Diffractive geometric optics Mathematics Subject Classification 200035B27 35J10  Download to read the full article text



Autor: Grégoire Allaire - Mariapia Palombaro - Jeffrey Rauch

Fuente: https://link.springer.com/



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