Lifespan estimates of solutions to semilinear wave equations with damping term on the exterior domain

Abstract

ABSTRACT Initial-boundary value problems for semilinear wave equations with damping term and Neumann boundary conditions on the exterior domain are investigated. In sub-critical and critical cases, blow-up and upper bound lifespan estimates of solutions to the problems which contain power nonlinearity , derivative nonlinearity , combined nonlinearity , respectively, are derived by applying test function technique and iterative method. The novelty is that lifespan estimates of solutions are associated with the well-known Strauss conjecture and Glassey conjecture.