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University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Wave propagation in periodic media and dispersive effects

## Wave propagation in periodic media and dispersive effectsAdd to your list(s) Download to your calendar using vCal - GrĂ©goire Allaire, Ecole Polytechnique
- Friday 27 March 2015, 15:00-16:00
- CMS, MR13.
If you have a question about this talk, please contact Harsha Hutridurga. We study high frequency wave propagation in a periodic medium for times long enough so that dispersive effects are important. In other words, we consider the homogenization of the wave equation in a periodic medium for long times of the order of the inverse of the period, and for 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 large group velocity with envelope functions which obey a Schrodinger 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 Schrodinger equation. This is a joint work with Mariapia Palombaro and Jeff Rauch. This talk is part of the Geometric Analysis and Partial Differential Equations seminar series. ## This talk is included in these lists:- All CMS events
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