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Diffraction of Bloch Wave Packets in periodic media

Jeudi, 7 Février, 2013 - 16:30
Prénom de l'orateur: 
Grégoire
Nom de l'orateur: 
Allaire
Résumé: 

This is a joint work with M. Palombaro and J. Rauch.
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 inital 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 Schr\{o}dinger type equation.

Institution: 
Ecole Polytechnique
Salle: 
Amphi Chabauty
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