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Analysis Seminar

Thursday, March 4, 2021
9:00am to 9:55am
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Stability results for anisotropic systems of wave equations
John Anderson, Department of Mathematics, Princeton University,

In this talk, I will describe a global stability result for a nonlinear anisotropic system of wave equations. This is motivated by studying phenomena involving characteristics with multiple sheets. For the proof, I will describe a strategy for controlling the solution based on bilinear energy estimates. Through a duality argument, this will allow us to prove decay in physical space using decay estimates for the homogeneous wave equation as a black box. The final proof will also require us to exploit a certain null condition that is present when the anisotropic system of wave equations satisfies a structural property involving the light cones of the equations.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.