Global existence, blow up and asymptotic behaviour of solutions for nonlinear Klein-Gordon equation with dissipative term

2009 ◽  
Vol 33 (7) ◽  
pp. 831-844 ◽  
Author(s):  
Xu Runzhang
Keyword(s):  
Global Existence ◽  
Asymptotic Behaviour ◽  
Gordon Equation ◽  
Blow Up ◽  
Dissipative Term ◽  
Asymptotic Behaviour Of Solutions ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Global Existence and Blow-Up of Solutions for Nonlinear Klein-Gordon Equation with Damping Term and Nonnegative Potentials

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wen-Yi Huang ◽  
Wen-Li Chen
Keyword(s):  
Global Existence ◽  
Gordon Equation ◽  
Blow Up ◽  
Global Solutions ◽  
Invariant Sets ◽  
Potential Well ◽  
Damping Term ◽  
Potential Wells ◽  
Klein Gordon ◽  
Klein Gordon Equation

This paper is concerned with the nonlinear Klein-Gordon equation with damping term and nonnegative potentials. We introduce a family of potential wells and discuss the invariant sets and vacuum isolating behavior of solutions. Using the potential well argument, we obtain a new existence theorem of global solutions and a blow-up result for solutions in finite time.

scholarly journals Revised concavity method and application to Klein-Gordon equation

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 831-839 ◽  
Author(s):  
M. Dimova ◽  
N. Kolkovska ◽  
N. Kutev
Keyword(s):  
Differential Inequality ◽  
Gordon Equation ◽  
Blow Up ◽  
Global Solutions ◽  
Initial Energy ◽  
Necessary And Sufficient Condition ◽  
Positive Initial Energy ◽  
Klein Gordon ◽  
Necessary And Sufficient ◽  
Klein Gordon Equation

A revised version of the concavity method of Levine, based on a new ordinary differential inequality, is proposed. Necessary and sufficient condition for nonexistence of global solutions of the inequality is proved. As an application, finite time blow up of the solution to Klein-Gordon equation with arbitrary positive initial energy is obtained under very general structural conditions.

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