Blow-up of positive-initial-energy solutions for nonlinearly damped semilinear wave equations

Abstract

. We consider a class of semilinear wave equations with both strongly and nonlinear weakly damped terms, u tt − ∆ u − ω ∆ u t + µ | u t | m − 2 u t = | u | p − 2 u, associated with initial and Dirichlet boundary conditions. Under certain con- ditions, we show that any solution with arbitrarily high positive initial energy blows up in finite time if m < p . Furthermore, we obtain a lower bound for the blow-up time.