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,associated with initial and Dirichlet boundary conditions. Under certain conditions, 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.