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

Keywords

• strongly damped wave equation
• time-dependent coefficients
• singular dissipation
• global well-posedness
• blow-up
• 35l05
• 35l71
• 35a01