Existence and uniqueness of solution of the Cauchy problem for singular systems of integro-differential equations

1993 ◽  
Vol 45 (12) ◽  
pp. 1932-1937
Author(s):  
Z. Šmarda
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Singular Systems ◽  
Uniqueness Of Solution ◽  
The Cauchy Problem

On mild solutions of gradient systems in Hilbert spaces

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Andrzej Rozkosz
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Representation ◽  
Infinite Dimensional ◽  
The Cauchy Problem

AbstractWe consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.

scholarly journals Existence and uniqueness of weak solutions of the Cauchy problem for parabolic delay-differential equations

1980 ◽  
Vol 21 (1) ◽  
pp. 65-80 ◽  
Author(s):  
S. Nababan ◽  
K.L. Teo
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Divergence Form ◽  
Partial Delay ◽  
The Cauchy Problem ◽  
Delay Differential

In this paper, a class of systems governed by second order linear parabolic partial delay-differential equations in “divergence form” with Cauchy conditions is considered. Existence and uniqueness of a weak solution is proved and its a priori estimate is established.

Global well-posedness of the Cauchy problem for system of oscillators on 2D-lattice with power potentials

2019 ◽  
Vol 16 (4) ◽  
pp. 465-476 ◽  
Author(s):  
Sergiy Bak
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite System ◽  
Global Solutions ◽  
Nonlinear Oscillators ◽  
Well Posedness ◽  
Two Dimensional ◽  
Coupled Nonlinear Oscillators ◽  
The Cauchy Problem

We consider an infinite system of ordinary differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on a two-dimensional integer-valued lattice. We prove a result on the existence and uniqueness of global solutions of the Cauchy problem for such systems with power potentials. Moreover, a result on the nonexistence of global solutions is obtained.

scholarly journals Landau-Lifshitz equation of ferromagnetism with external magnetic field

2002 ◽  
Vol 72 (3) ◽  
pp. 299-316 ◽  
Author(s):  
P. Y. H. Pang ◽  
J. Xiao ◽  
F. Zhou
Keyword(s):  
Magnetic Field ◽  
Cauchy Problem ◽  
External Magnetic Field ◽  
Existence And Uniqueness ◽  
Blow Up ◽  
Uniqueness Of Solution ◽  
Energy Identity ◽  
Lifshitz Equation ◽  
The Cauchy Problem

AbstractIn this article, we prove the existence and uniqueness of solution for the Cauchy problem of the Landau-Lifshitz equation of ferromagnetism with external magnetic field. We also show that the solution is globally regular with the exception of at most finitely many blow-up points. An energy identity at blow-up points is presented.

scholarly journals On the solvability of the modified Cauchy problem for linear systems of generalized ordinary differential equations with singularities

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Malkhaz Ashordia ◽  
Inga Gabisonia ◽  
Mzia Talakhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Unique Solvability ◽  
Sufficient Conditions ◽  
The Cauchy Problem ◽  
Generalized Ordinary Differential Equations

AbstractEffective sufficient conditions are given for the unique solvability of the Cauchy problem for linear systems of generalized ordinary differential equations with singularities.

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

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