scholarly journals Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D

2018 ◽  
Vol 38 (3) ◽  
pp. 1479-1504 ◽  
Author(s):  
Shinya Kinoshita ◽  
Keyword(s):  
Cauchy Problem ◽  
Well Posedness ◽  
Zakharov System ◽  
The Cauchy Problem ◽  
Klein Gordon

Local well-posedness for the quantum Zakharov system in three and higher dimensions

2021 ◽  
Vol 18 (02) ◽  
pp. 257-270
Author(s):  
Isao Kato
Keyword(s):  
Cauchy Problem ◽  
Type System ◽  
Higher Dimensions ◽  
Well Posedness ◽  
Zakharov System ◽  
Quantum Parameter ◽  
Fourier Restriction ◽  
The Cauchy Problem ◽  
The One ◽  
Quantum Zakharov System

We study the Cauchy problem associated with a quantum Zakharov-type system in three and higher spatial dimensions.Taking the quantum parameter to unit and developing Fourier restriction norm arguments, we establish local well-posedness property for wider range than the one known for the Zakharov system.

scholarly journals Klein-Gordon Equations on Modulation Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Guoping Zhao ◽  
Jiecheng Chen ◽  
Weichao Guo
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Stability Theory ◽  
Scattering Theory ◽  
Modulation Spaces ◽  
Well Posedness ◽  
Blowup Criterion ◽  
The Cauchy Problem ◽  
Klein Gordon

We consider the Cauchy problem for a family of Klein-Gordon equations with initial data in modulation spacesMp,1a. We develop the well-posedness, blowup criterion, stability of regularity, scattering theory, and stability theory.

scholarly journals THE CAUCHY PROBLEM FOR METRIC-AFFINE f(R)-GRAVITY IN PRESENCE OF A KLEIN–GORDON SCALAR FIELD

2011 ◽  
Vol 08 (01) ◽  
pp. 167-176 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
S. VIGNOLO
Keyword(s):  
Cauchy Problem ◽  
Scalar Field ◽  
Sufficient Conditions ◽  
Well Posedness ◽  
Field Equations ◽  
Initial Value ◽  
The Cauchy Problem ◽  
Klein Gordon

We study the initial value formulation of metric-affine f(R)-gravity in presence of a Klein–Gordon scalar field acting as source of the field equations. Sufficient conditions for the well-posedness of the Cauchy problem are formulated. This result completes the analysis of the same problem already considered for other sources.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

scholarly journals Multidimensional van der Corput-Type estimates involving Mittag-Leffler functions

2020 ◽  
Vol 23 (6) ◽  
pp. 1663-1677
Author(s):  
Michael Ruzhansky ◽  
Berikbol T. Torebek
Keyword(s):  
Cauchy Problem ◽  
Exponential Function ◽  
Evolution Equations ◽  
Oscillatory Integrals ◽  
Schrödinger Equations ◽  
Fractional Evolution Equations ◽  
Type Function ◽  
Fractional Schrödinger Equations ◽  
The Cauchy Problem ◽  
Klein Gordon

Abstract The paper is devoted to study multidimensional van der Corput-type estimates for the intergrals involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study multidimensional oscillatory integrals appearing in the analysis of time-fractional evolution equations. More specifically, we study two types of integrals with functions E α, β (i λ ϕ(x)), x ∈ ℝ N and E α, β (i α λ ϕ(x)), x ∈ ℝ N for the various range of α and β. Several generalisations of the van der Corput-type estimates are proved. As an application of the above results, the Cauchy problem for the multidimensional time-fractional Klein-Gordon and time-fractional Schrödinger equations are considered.

scholarly journals The cauchy problem for non-linear Klein-Gordon equations

1993 ◽  
Vol 152 (3) ◽  
pp. 433-478 ◽  
Author(s):  
Jacques C. H. Simon ◽  
Erik Taflin
Keyword(s):  
Cauchy Problem ◽  
Non Linear ◽  
The Cauchy Problem ◽  
Klein Gordon
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