Nonlinear wave equations on time dependent inhomogeneous backgrounds

Abstract

In this thesis, I study the nonlinear wave equations on a class of asymptotically flat Lorentzian manifolds (R<super>3+1<\super>, <italic>g<\italic>) with <bold>time dependent<\bold> inhomogeneous metric <italic>g<\italic>.

Based on a new approach for proving the decay of solutions of linear wave equations, I give several applications to nonlinear problems. In particular, I show the small data global existence result for quasilinear wave equations satisfying the null condition on a class of time dependent inhomogeneous backgrounds which do not settle to any

particular stationary metric.