Mathematics Colloquia and Seminars

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In this talk, I will describe stability results for certain systems of anisotropic wave equations. These kinds of equations arise in optics, and are more generally motivated by a desire to understand hyperbolic equations whose characteristics have multiple sheets. For the proof, I will describe a strategy for proving decay that relies on bilinear energy estimates and duality arguments. The proof also requires us to use nonlinear structure which comes from the geometry of the light cones. If time permits, I will also describe forthcoming work with Samuel Zbarsky, which uses bilinear energy estimates and duality to get a finer phase space understanding of solutions to nonlinear equations.