Global solution and blow-up of logarithmic Klein-Gordon equation
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 281-294
https://doi.org/10.4134/BKMS.b190190
Published online March 31, 2020
Yaojun Ye
Zhejiang University of Science and Technology
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.
Keywords : Klein-Gordon equation, logarithmic nonlinearity, global solution, exponential decay, blow-up
MSC numbers : Primary 35L05, 35L10, 35B40
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