On uniqueness of solutions to the Cauchy problem for degenerate Fokker–Planck–Kolmogorov equations

2013 ◽  
Vol 13 (3) ◽  
pp. 577-593 ◽  
Author(s):  
Vladimir I. Bogachev ◽  
Michael Röckner ◽  
Stanislav V. Shaposhnikov
Keyword(s):  
Cauchy Problem ◽  
Kolmogorov Equations ◽  
Uniqueness Of Solutions ◽  
The Cauchy Problem ◽  
Fokker Planck

scholarly journals On the superposition principle for Fokker-Planck-Kolmogorov equations

2019 ◽  
Vol 487 (5) ◽  
pp. 483-486
Author(s):  
V. I. Bogachev ◽  
M. Röckner ◽  
S. V. Shaposhnikov
Keyword(s):  
Cauchy Problem ◽  
Superposition Principle ◽  
Martingale Problem ◽  
Kolmogorov Equation ◽  
Kolmogorov Equations ◽  
The Cauchy Problem ◽  
Fokker Planck

We give a generalization of the so-called superposition principle for probability solutions to the Cauchy problem for the Fokker-Planck-Kolmogorov equation, according to which such a solution is generated by a solution to the corresponding martingale problem.

scholarly journals Existence and Uniqueness of Solutions for a Type of Generalized Zakharov System

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rui Li ◽  
Xing Lin ◽  
Zongwei Ma ◽  
Jingjun Zhang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Energy Conservation ◽  
Classical Solution ◽  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Zakharov System ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We study the Cauchy problem for a type of generalized Zakharov system. With the help of energy conservation and approximate argument, we obtain global existence and uniqueness in Sobolev spaces for this system. Particularly, this result implies the existence of classical solution for this generalized Zakharov system.

Some Results for the Davey-Stewartson System on a Circle

2012 ◽  
Vol 204-208 ◽  
pp. 4429-4432
Author(s):  
Tsai Jung Chen ◽  
Yung Fu Fang ◽  
Ying Ji Hong
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
System Model ◽  
Mathematical Aspect ◽  
Uniqueness Of Solutions ◽  
Apriori Estimates ◽  
The Cauchy Problem

In this paper we consider the Cauchy problem of the Davey-Stewartson system on a circle. We establish, from a mathematical aspect, certain apriori estimates necessary to ensure the existence and uniqueness of solutions of the Davey-Stewartson system model.

THE GLOBAL CLASSICAL SOLUTION OF THE VLASOV–MAXWELL–FOKKER–PLANCK SYSTEM NEAR MAXWELLIAN

2011 ◽  
Vol 21 (05) ◽  
pp. 1007-1025 ◽  
Author(s):  
MYEONGJU CHAE
Keyword(s):  
Cauchy Problem ◽  
Electromagnetic Field ◽  
Classical Solution ◽  
Charged Particles ◽  
Classical Solutions ◽  
Global Classical Solution ◽  
Self Consistent ◽  
The Cauchy Problem ◽  
Fokker Planck

The Vlasov–Maxwell–Fokker–Planck system is used in modeling distribution of charged particles in plasma, where particles interact via collisions and through their self-consistent electromagnetic field. We prove the existence of global in time classical solutions to the Cauchy problem near Maxwellians.

The Exact Solution of the Cauchy Problem for Two Generalized Fokker-Planck Equations — Algebraic Approach

1997 ◽  
Vol 12 (01) ◽  
pp. 165-170 ◽  
Author(s):  
A. A. Donkov ◽  
A. D. Donkov ◽  
E. I. Grancharova
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Algebraic Approach ◽  
Planck Equation ◽  
Operational Method ◽  
Suzuki Method ◽  
Fokker Planck Equation ◽  
The Cauchy Problem ◽  
Fokker Planck Equations ◽  
Fokker Planck

By employing algebraic techniques we find the exact solutions of the Cauchy problem for two equations, which may be considered as n-dimensional generalization of the famous Fokker–Planck equation. Our approach is a combination of the disentangling techniques of R. Feynman with operational method developed in modern functional analysis in particular in the theory of partial differential equations. Our method may be considered as a generalization of the M. Suzuki method of solving the Fokker–Planck equation.

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