Stability results for anisotropic systems of wave equations

Abstract: This talk 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 as encountered in, for example, the study of light in a biaxial crystal. For the proof, we control the solution using 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 use nonlinear structure that is present when the anisotropic system of wave equations satisfies a condition involving the light cones of the equations.