On a strongly damped semilinear wave equation with time-varying source and singular dissipation

Abstract This paper deals with the global well-posedness and blow-up phenomena for a strongly damped semilinear wave equation time-varying source singular dissipative terms under null Dirichlet boundary condition. On basis of cut-off technique, multiplier method, contraction mapping principle, modified potential well we establish local obtain threshold between existence nonexistence solution (including critical case). Meanwhile, aid differential inequality result solutions arbitrarily positive initial energy lifespan are derived.