Blow-Up of Solutions to Semilinear Nonautonomous Wave Equations with Robin Boundary Conditions

Abstract

The problem of the blow-up of solutions to the initial boundary value problem for a nonautonomous semilinear wave equation with damping and accelerating terms under the Robin boundary condition is studied. Sufficient conditions for the blow up in finite time of solutions to semilinear damped wave equations with arbitrary large initial energy are obtained. A result on the blow-up of solutions with negative initial energy to a semilinear second-order wave equation with an accelerating term is also obtained.