Stabilization of the critical semilinear wave equation with Dirichlet-Neumann boundary condition on bounded domain

Abstract

We study the stability of the critical defocusing semilinear wave equation with a distributed locally damping and Dirichlet-Neumann boundary condition on a bounded domain. The main novelty is to establish a framework to study the stability of the damped critical semilinear wave equation on bounded domain. The unique continuation properties and the observability inequalities are proved by the Morawetz estimates in Euclidean spaces, and then the compactness-uniqueness arguments are applied to prove the main stabilization result.