On the Collapse of Solutions of the Cauchy Problem for the Cubic Schrödinger Evolution Equation

2019 ◽  
Vol 105 (1-2) ◽  
pp. 64-70 ◽  
Author(s):  
Sh. M. Nasibov
Keyword(s):  
Cauchy Problem ◽  
Evolution Equation ◽  
The Cauchy Problem

scholarly journals Construction of a solution of a certain evolution equation

1977 ◽  
Vol 66 ◽  
pp. 23-36 ◽  
Author(s):  
Akinobu Shimizu
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Brownian Motion ◽  
Differential Operator ◽  
Evolution Equation ◽  
Partial Differential Operator ◽  
Initial Condition ◽  
Uniqueness Of Solutions ◽  
One Dimensional ◽  
The Cauchy Problem

Let us consider the stochastic differential equation,with initial condition,where Bt, t ≧ 0,is a one-dimensional Brownian motion, and Lxis a second order uniformly elliptic partial differential operator satisfying some additional conditions that will be described in §2. The existence and the uniqueness of solutions of the Cauchy problem have been established by B. L. Rozovskii [8].

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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