GLOBAL EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR COUPLED NONLINEAR WAVE EQUATIONS WITH DAMPING AND SOURCE TERMS

• Ye, Yaojun
• Received : 2013.10.11
• Published : 2014.11.30
• 70 7

Abstract

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

Keywords

systems of nonlinear wave equations;damping and source terms;global solutions;blow-up;lifespan of solutions

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Acknowledgement

Supported by : National Natural Science Foundation of China, The Natural Science Foundation of Zhejiang Province