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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.

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