Global existence for quasilinear wave equations exterior to star-shaped regions with inhomogeneous boundary conditions

Abstract

This paper establishes the global existence of classical solutions to systems of nonlinear wave equations with multiple speeds outside star-shaped regions satisfying time-independent inhomogeneous boundary conditions, provided that nonlinear terms obey the null condition. We first prove the existence and uniqueness of stationary solutions. Then we use the space-time estimates for perturbed wave equations in Metcalfe and Sogge (2007) to show that solutions of systems converge to stationary solutions as time goes to infinity.