Blow-up for a damped p-Laplacian type wave equation with logarithmic nonlinearity

Abstract

In this paper, a damped p-Laplacian type wave equation with logarithmic nonlinearity is considered and finite time blow-up of solutions is proved with initial data at different initial energy levels. More precisely, when the initial energy is subcritical, a sufficient condition for the solutions to blow up in finite time is derived, by combining the Nehari manifold with concavity argument. When the initial energy is supercritical, some new skills are invented to establish another finite time blow-up criterion for this problem. Meanwhile, for each of the above two cases, the lifespan of the weak solutions is estimated from above. Moreover, by making full use of the strongly damping term and choosing appropriate parameters, a lower bound for the blow-up time is given.