耗散线性Boltzmann方程的解的正则性

数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1662-1668.

耗散线性Boltzmann方程的解的正则性

晋守博|陈攀峰|孙善辉

1.宿州学院智能信息处理实验室 |安徽宿州 234000;
2.宿州学院数学与统计学院 |安徽宿州 234000

收稿日期:2010-11-24 修回日期:2011-12-06 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
宿州学院智能信息处理实验室开放课题(2011YKF12, 2011YKF14)和安徽省高校优秀青年人才基金(2011SQRL153)资助

Regularity of the Solution to the Dissipative Linear Boltzmann Equation

JIN Shou-Bo, CHEN Pan-Feng, SUN Shan-Hui

1.Laboratory of Intelligent Information Processing, Suzhou University, Anhui Suzhou 234000;
2.School of Mathematics and Statistics, Suzhou University, Anhui Suzhou 234000

Received:2010-11-24 Revised:2011-12-06 Online:2011-12-25 Published:2011-12-25
Supported by:
宿州学院智能信息处理实验室开放课题(2011YKF12, 2011YKF14)和安徽省高校优秀青年人才基金(2011SQRL153)资助

摘要/Abstract

摘要：

该文讨论了一种与特定背景介质发生耗散碰撞的稀薄气体的线性Boltzmann方程, 当该方程的碰撞核具有拟Maxwell形式时, 考查了方程的解的正则性, 证明了当气体的初始分布f₀(v)具有有限温度时, 如果f₀(v)∈H^∞(R³), 那么耗散线性Boltzmann方程的解f(v, t)∈H^∞(R³).

关键词: 线性Boltzmann方程, 正则性, Sobolev空间, 傅里叶变换

Abstract:

This paper discusses a linear Boltzmann equation describing dissipative interactions of a gas of test particles with a fixed background. For a pseudo-Maxwellian collision kernel, it is proved that, if the initial distribution has finite temperature and f₀(v)∈H^∞(R³), the solution f(v, t) of Boltzmann equation belongs to Sobolev space H^∞(R³).

Key words: Linear Boltzmann equation, Regularity, Sobolev space, Fourier transform

中图分类号:

35Q58

晋守博, 陈攀峰, 孙善辉. 耗散线性Boltzmann方程的解的正则性[J]. 数学物理学报, 2011, 31(6): 1662-1668.

JIN Shou-Bo, CHEN Pan-Feng, SUN Shan-Hui. Regularity of the Solution to the Dissipative Linear Boltzmann Equation[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1662-1668.

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