Global existence,blow up and asymptotic behaviour of solutions for nonlinear Klein–Gordon equation with dissipative term |
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| Authors: | Xu Runzhang |
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| Institution: | 1. College of Science, Harbin Engineering University, Harbin 150001, People's Republic of China;2. College of Automation, Harbin Engineering University, Harbin 150001, People's Republic of China;3. Differential Equations Research Center, Harbin Engineering University, Harbin 150001, People's Republic of China |
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| Abstract: | We study the Cauchy problem of nonlinear Klein–Gordon equation with dissipative term. By introducing a family of potential wells, we derive the invariant sets and prove the global existence, finite time blow up as well as the asymptotic behaviour of solutions. In particular, we show a sharp condition for global existence and finite time blow up of solutions. Copyright © 2009 John Wiley & Sons, Ltd. |
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| Keywords: | nonlinear Klein– Gordon equation dissipative potential wells global existence blow up asymptotic behaviour |
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