scholarly journals The Cauchy problem for a modified Euler-Poisson system in one dimension

2021 ◽  
pp. 1
Author(s):  
Long Wei
Keyword(s):  
Cauchy Problem ◽  
One Dimension ◽  
Poisson System ◽  
The Cauchy Problem

THE IVP FOR THE SCHRÖDINGER–POISSON-Xα EQUATION IN ONE DIMENSION

2005 ◽  
Vol 15 (08) ◽  
pp. 1169-1180 ◽  
Author(s):  
H. P. STIMMING
Keyword(s):  
Cauchy Problem ◽  
Quantum System ◽  
Existence And Uniqueness ◽  
Space Dimension ◽  
Semiclassical Limit ◽  
Semigroup Theory ◽  
One Dimension ◽  
The Cauchy Problem ◽  
Electron Quantum ◽  
Particle Approximation

The Schrödinger–Poisson-Xα equation is an effective one-particle approximation of a many-electron quantum system. In space dimension d<3, existence analysis for this equation is not contained in standard results for nonlinear Schrödinger equations. We obtain existence and uniqueness of the Cauchy problem in d = 1 using semigroup theory. Furthermore, we discuss the semiclassical limit.

On the Cauchy problem for one dimension generalized Boussinesq equation

2015 ◽  
Vol 26 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Yinxia Wang
Keyword(s):  
Cauchy Problem ◽  
Boussinesq Equation ◽  
Nonlinear Approximation ◽  
Global Solutions ◽  
One Dimension ◽  
Diffusion Waves ◽  
Self Similar Solution ◽  
The Cauchy Problem ◽  
Nonlinear Diffusion Waves ◽  
Generalized Boussinesq Equation

In this paper, we study the Cauchy problem for one dimension generalized damped Boussinesq equation. First, global existence and decay estimate of solutions to this problem are established. Second, according to the detail analysis for solution operator the generalized damped Boussinesq equation, the nonlinear approximation to global solutions is established. Finally, we prove that the global solution u to our problem is asymptotic to the superposition of nonlinear diffusion waves expressed in terms of the self-similar solution of the viscous Burgers equation as time tends to infinity.

scholarly journals The Cauchy Problem for the 3-D Vlasov–Poisson System with Point Charges

2011 ◽  
Vol 201 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Carlo Marchioro ◽  
Evelyne Miot ◽  
Mario Pulvirenti
Keyword(s):  
Cauchy Problem ◽  
Poisson System ◽  
The Cauchy Problem

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.

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