Well-posedness and uniform decay rates for the Klein–Gordon equation with damping term and acoustic boundary conditions

2009 ◽  
Vol 50 (1) ◽  
pp. 013506 ◽  
Author(s):  
Jong Yeoul Park ◽  
Tae Gab Ha
Keyword(s):  
Boundary Conditions ◽  
Gordon Equation ◽  
Decay Rates ◽  
Well Posedness ◽  
Damping Term ◽  
Acoustic Boundary Conditions ◽  
Uniform Decay ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm

2011 ◽  
Vol 30 (3) ◽  
pp. 573-621 ◽  
Author(s):  
M. Keel ◽  
◽  
Tristan Roy ◽  
Terence Tao ◽  
◽  
...  
Keyword(s):  
Gordon Equation ◽  
Energy Norm ◽  
Well Posedness ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass

2021 ◽  
Author(s):  
Luca Nanni
Keyword(s):  
General Solution ◽  
Wave Packet ◽  
Boundary Conditions ◽  
Theoretical Investigation ◽  
Wave Equations ◽  
Gordon Equation ◽  
Fourier Integral ◽  
Klein Gordon ◽  
Group Velocities ◽  
Klein Gordon Equation

In this article, the general solution of the tachyonic Klein-Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex \omega-plane. In particular, it is proved that under given boundary conditions this solution does not contain any superluminal components. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that for enough small energies it behaves as a localized wave.

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.

BILINEAR ESTIMATES AND APPLICATIONS TO GLOBAL WELL-POSEDNESS FOR THE DIRAC–KLEIN–GORDON EQUATION ON ℝ1+1

2013 ◽  
Vol 10 (01) ◽  
pp. 1-35 ◽  
Author(s):  
TIMOTHY CANDY
Keyword(s):  
Global Existence ◽  
Gordon Equation ◽  
Well Posedness ◽  
Bilinear Estimates ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Nonlinear Dirac Equations ◽  
Klein Gordon Equation

We prove new bilinear estimates for the [Formula: see text] spaces which are optimal up to endpoints. These estimates are often used in the theory of nonlinear Dirac equations on ℝ1+1. As an application, by using the I-method of Colliander, Keel, Staffilani, Takaoka and Tao, we extend the work of Tesfahun on global existence below the charge class for the Dirac–Klein–Gordon equation on ℝ1+1.

scholarly journals Theoretical Investigation of Subluminal Particles Endowed with Imaginary Mass

Particles ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 325-332
Author(s):  
Luca Nanni
Keyword(s):  
General Solution ◽  
Wave Packet ◽  
Boundary Conditions ◽  
Wave Equations ◽  
Gordon Equation ◽  
Fourier Integral ◽  
Klein Gordon ◽  
The Given ◽  
Group Velocities ◽  
Klein Gordon Equation

In this article, the general solution of the tachyonic Klein–Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex ω-plane. In particular, it is proved that this solution does not contain any superluminal components under the given boundary conditions. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of the neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that it behaves as a localized wave for sufficiently small energies.

Sign in / Sign up

Export Citation Format

Share Document