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Abstract and Applied Analysis
Volume 2015, Article ID 318618, 9 pages
http://dx.doi.org/10.1155/2015/318618
Research Article

On the Fourier-Transformed Boltzmann Equation with Brownian Motion

Department of Mathematics, College of Natural Science, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul 156-756, Republic of Korea

Received 17 July 2014; Accepted 16 September 2014

Academic Editor: Xiao-Jun Yang

Copyright © 2015 Yong-Kum Cho and Eunsil Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish a global existence theorem, and uniqueness and stability of solutions of the Cauchy problem for the Fourier-transformed Fokker-Planck-Boltzmann equation with singular Maxwellian kernel, which may be viewed as a kinetic model for the stochastic time-evolution of characteristic functions governed by Brownian motion and collision dynamics.