Phase Space Analysis of Partial Differential Equations

Nonlinear Geometric Optics and Hyperbolic PDE

speaker: Jeffrey Rauch (Michigan University)

abstract: This minicourse is an introduction to the methods of nonlinear geometric optics. In part it will follow lecture notes which can be found on my web page. The goal is to start with the very simplest linear examples to motivate the various ansatz which serve to construct approximate solutions with error tending to zero as wavelength tends to zero. The "Phase Space " aspect comes from the fact that the solutions are rapidly oscillating and the pair position and direction of oscillation in the cotangent bundle creates the link. Propagation of this pair along null bicharacteritics corresponds to the laws of geometric optics going back to Fermat's principle of least time.

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