Stabilization of the critical semilinear wave equation on non-compact Riemannian manifold

Abstract

We study the stability of the defocusing critical semilinear wave equation with locally distributed damping in an exterior domain. Under some assumptions on the Riemannian metric, the geometric multiplier technique and the compactness-uniqueness arguments were used to prove the unique continuation, the observability inequality respectively. Then the energy decay of the nonlinear system was obtained.