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Sharp threshold of global existence for the Klein-Gordon equations with critical nonlinearity

✍ Scribed by Zai-hui Gan; Bo-ling Guo; Jian Zhang

Publisher: Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year: 2009
Tongue: English
Weight: 194 KB
Volume: 25
Category: Article
ISSN: 0168-9673
DOI: 10.1007/s10255-007-7085-7

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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 s