Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2020; 57(2): 281-294

Online first article February 27, 2020      Printed March 31, 2020

https://doi.org/10.4134/BKMS.b190190

Copyright © The Korean Mathematical Society.

Global solution and blow-up of logarithmic Klein-Gordon equation

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

Supported by: This work was financially supported by Natural Science Foundation of Zhejiang Province (No. LY17A010009).