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Wave propagation in periodic media and dispersive effects

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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 & Partial Differential Equations seminar series.

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