Asymptotics of the solutions to theN-particle Kolmogorov-Feller equations and the asymptotics of the solution to the Boltzmann equation in the region of large deviations |
| |
Authors: | V P Maslov |
| |
Institution: | (1) Moscow Institute of Electronics and Mathematics, USSR |
| |
Abstract: | We construct a representation in which the asymptotics of the solution to the Kolmogorov-Feller equation in the Fock space
Γ(L
1(ℝ
n
)) is of a form similar to the WKB asymptotic expansion; namely, the Boltzmann equation inL
1(ℝ
n
) plays the role of the Hamilton equations, the linearized Boltzmann equation extended to Γ(L
1(ℝ
n
)) plays the role of the transport equation, and the Hamilton-Jacobi equation follows from the conservation of the total probability
for the solutions of the Boltzmann equation. We also construct the asymptotics of the solution to the Boltzmann equation with
small transfer of momentum; this asymptotics is given by the tunnel canonical operator corresponding to the self-consistent
characteristic equation.
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 694–709, November, 1995.
The author is deeply grateful to Prof. A. M. Chebotarev, whose assistance has made the writing of this paper possible.
This work was financially supported by the International Science Foundation under grants Nos. MFO000 and MFO300. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|