Abstract
In this article we consider the Petrovsky equation u tt + Δ2 u − Δu t + |u t | m−1 u t = |u| p−1 u. We prove the global existence of the solution under conditions without any relation between m and p, and establish an exponential decay rate. We also show that the solution blows up in finite time if p > m and the initial energy is less than the potential well depth.
Acknowledgements
The authors wish to express their gratitude to the anonymous referees for a number of valuable comments and suggestions. This work was partly supported by the Tianyuan Fund of Mathematics (Grant No. 11026211) and the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No. 09KJB110005).