Blowup of solutions for evolution equations with nonlinear damping

Abstract

The initial boundary value problem for a class of evolution equations with nonlinear damping in a bounded domain is considered. By modifying the method in [8], we prove that any solution, with nonpositive initial energy as well as small positive initial energy, blows up in finite time under some conditions. The estimates of the lifespan of solutions are also given. We improve an earlier result in [12].