The APDE seminar on Monday, 3/8, will be given by John Anderson online via Zoom from 4:10 to 5:00pm. To participate, email Georgios Moschidis (email@example.com) or Federico Pasqualotto (firstname.lastname@example.org).
Title: Stability results for anisotropic systems of wave equations
Abstract: 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.