Sharp threshold of global existence and blow-up of the combined nonlinear Klein–Gordon equation

2019 ◽  
Vol 474 (2) ◽  
pp. 814-832 ◽  
Author(s):  
Jing Lu ◽  
Qianyun Miao
Keyword(s):  
Global Existence ◽  
Gordon Equation ◽  
Blow Up ◽  
Sharp Threshold ◽  
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.

Global Existence and Blowup for the Cubic Nonlinear Klein-Gordon Equations in Three Space Dimensions

2010 ◽  
Vol 10 (2) ◽  
Author(s):  
Jian Zhang ◽  
Zaihui Gan ◽  
Boling Guo
Keyword(s):  
Global Existence ◽  
Invariant Manifolds ◽  
Gordon Equation ◽  
Global Solutions ◽  
The Other ◽  
Cubic Nonlinearity ◽  
Sharp Threshold ◽  
Klein Gordon ◽  
Three Space ◽  
Klein Gordon Equation

AbstractIn this paper, we apply a cross-constrained variational method to study the classic nonlinear Klein-Gordon equation with cubic nonlinearity in three space dimensions. By constructing a type of cross-constrained variational problem and establishing the so-called cross invariant manifolds, we obtain a sharp threshold for blowup and global existence of the solution to the equation under study which is different from that in [10] . On the other hand, we give an answer to the question that how small the initial data have to be for the global solutions to exist.

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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