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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 3
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Original Articles

Global existence and blow-up of solutions for a strongly damped Petrovsky system with nonlinear damping

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Pages 575-586 | Received 10 May 2010, Accepted 19 Dec 2010, Published online: 09 Mar 2011
 

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.

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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).

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