Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GLOBAL SOLUTION AND BLOW-UP OF LOGARITHMIC KLEIN-GORDON EQUATION

  • Ye, Yaojun (Department of Mathematics and Information Science Zhejiang University of Science and Technology)
  • Received : 2019.02.17
  • Accepted : 2019.12.18
  • Published : 2020.03.31

Abstract

The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.

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Acknowledgement

Supported by : Natural Science Foundation of Zhejiang Province

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