Global existence and blow up of the solution for nonlinear Klein-Gordon equation with variable coefficient nonlinear source term
- Resource Type
- article
- Authors
- Sun Cong; Yan Dong Ze; Zhang Yong Ling
- Source
- Open Mathematics, Vol 20, Iss 1, Pp 931-945 (2022)
- Subject
- klein-gordon equation
global existence of the solutions
blow up of the solutions
potential well method
energy estimation method
35j05
35j09
35j10
Mathematics
QA1-939
- Language
- English
- ISSN
- 2391-5455
This article is devoted to study the existence of global solutions and finite time blow-up of local solution for nonlinear Klein-Gordon equation with variable coefficient nonlinear source term. By applying the potential well and energy estimation method, in low initial energy and critical initial energy, we derive some sufficient conditions which are global existence and explosion of the solutions for this type of Klein-Gordon equation.