scholarly journals On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces

2021 ◽  
pp. 1
Author(s):  
L. Chaichenets ◽  
N. Pattakos
Keyword(s):  
Initial Data ◽  
Gordon Equation ◽  
Modulation Spaces ◽  
Global Wellposedness ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals On the Exact Boundary Control for the Linear Klein-Gordon Equation in Non-cylindrical Domains

2020 ◽  
Vol 21 (2) ◽  
pp. 371
Author(s):  
R. S. O. Nunes
Keyword(s):  
Initial Data ◽  
Wave Operator ◽  
Gordon Equation ◽  
Controllability Problem ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Exact Boundary ◽  
Cylindrical Domains ◽  
Klein Gordon ◽  
Klein Gordon Equation

The purpose of this paper is to study an exact boundary controllability problem in noncylindrical domains for the linear Klein-Gordon equation. Here, we work near of the extension techniques presented By J. Lagnese in [12] which is based in the Russell’s controllability method. The control time is obtained in any time greater then the value of the diameter of the domain on which the initial data are supported. The control is square integrable and acts on whole boundary and it is given by conormal derivative associated with the above-referenced wave operator.

scholarly journals A REMARK ON LONG RANGE SCATTERING FOR THE NONLINEAR KLEIN–GORDON EQUATION

2005 ◽  
Vol 02 (01) ◽  
pp. 77-89 ◽  
Author(s):  
HANS LINDBLAD ◽  
AVY SOFFER
Keyword(s):  
Asymptotic Expansion ◽  
Initial Data ◽  
Long Range ◽  
Gordon Equation ◽  
Scattering Problem ◽  
One Dimension ◽  
Complete Asymptotic Expansion ◽  
Arbitrary Size ◽  
Klein Gordon ◽  
Klein Gordon Equation

We consider the scattering problem for the nonlinear Klein–Gordon Equation with long range nonlinearity in one dimension. We prove that for all prescribed asymptotic solutions there is a solution of the equation with such behavior, for some choice of initial data. In the case the nonlinearity has the good sign (repulsive) the result hold for arbitrary size asymptotic data. The method of proof is based on reducing the long range phase effects to an ODE; this is done via an appropriate ansatz. We also find the complete asymptotic expansion of the solutions.

scholarly journals The Initial Value Problem for the Quadratic Nonlinear Klein-Gordon Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-35 ◽  
Author(s):  
Nakao Hayashi ◽  
Pavel I. Naumkin
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Compact Support ◽  
Initial Value Problem ◽  
Normal Forms ◽  
Gordon Equation ◽  
Initial Value ◽  
Klein Gordon ◽  
Klein Gordon Equation

We study the initial value problem for the quadratic nonlinear Klein-Gordon equation , , , , where and . Using the Shatah normal forms method, we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.

Mixed Norm Decay for the Klein-Gordon Equation with Initial Data in Lp

1986 ◽  
Vol 29 (1) ◽  
pp. 11-19
Author(s):  
Bernard Marshall
Keyword(s):  
Initial Data ◽  
Gordon Equation ◽  
Necessary Conditions ◽  
Mixed Norm ◽  
Norm Estimates ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractThis paper gives necessary conditions for mixed norm estimates from Lp to Lr (Lq) for solutions of the Klein-Gordon equationThese conditions are best possible if p = 2 or

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation
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