The Cauchy problem for BBGKY hierarchy of quantum kinetic equations with Coulomb potential

2012 ◽  
Author(s):  
M. Brokate ◽  
M. Yu. Rasulova
Keyword(s):  
Cauchy Problem ◽  
Coulomb Potential ◽  
Kinetic Equations ◽  
Bbgky Hierarchy ◽  
The Cauchy Problem

The Cauchy problem for BBGKY hierarchy of quantum kinetic equations with coulomb potential

2009 ◽  
Author(s):  
M. Brokate ◽  
M. Yu. Rasulova ◽  
A. H. Siddiqi ◽  
M. Brokate ◽  
A. K. Gupta
Keyword(s):  
Cauchy Problem ◽  
Coulomb Potential ◽  
Kinetic Equations ◽  
Bbgky Hierarchy ◽  
The Cauchy Problem

A modified truncation procedure for the BBGKY hierarchy

1969 ◽  
Vol 3 (1) ◽  
pp. 107-118 ◽  
Author(s):  
C. J. Myerscough
Keyword(s):  
Kinetic Equation ◽  
Physical Interpretation ◽  
Coulomb Potential ◽  
Kinetic Equations ◽  
Bbgky Hierarchy ◽  
Collision Integral ◽  
The Other ◽  
Standard Methods ◽  
Particle Separations ◽  
Number Of Authors

The approximations usually made to truncate the BBGKY hierarchy for a plasma are discussed; their failure at small inter-particle separations leads to divergence of the Balescu—Lenard collision integral. A number of authors have obtained convergent kinetic equations, often by rather complicated methods.It is shown here that, if the standard truncation procedure is modified in a way which makes it less obviously inconsistent for close approaches, the standard methods maybe closely followed in deriving a convergent collision integral which agrees to dominant order with the ‘cutoff’ Balescu—Lenard integral and with the other work on the problem. In fact, the kinetic equation obtained is identical with the Balescu—Lenard equation except that the Coulomb potential is replaced by another that is non-singular at the origin. A physical interpretation of this result is suggested.

scholarly journals The generalized kinetic equation for symmetric particle systems

2012 ◽  
Vol 110 (1) ◽  
pp. 140
Author(s):  
Halyna M. Hubal
Keyword(s):  
Cauchy Problem ◽  
Kinetic Equation ◽  
Pair Potential ◽  
Bbgky Hierarchy ◽  
Particle Systems ◽  
Symmetric System ◽  
The Cauchy Problem ◽  
Generalized Kinetic Equation ◽  
Many Particles

The generalized kinetic equation is obtained for symmetric system of many particles interacting via a pair potential. A representation of a solution of the Cauchy problem for the BBGKY hierarchy is used in the form of an expansion over particle groups whose evolution is governed by the cumulants (semi-invariants).

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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