Boltzmann方程的永久型解

数学物理学报

Boltzmann方程的永久型解

魏金波; 张显文

华中科技大学数学系武汉 430074

收稿日期:2004-09-20 修回日期:2005-07-07 出版日期:2007-04-25 发布日期:2007-04-25
通讯作者: 魏金波
基金资助:
国家自然科学基金(10571066)及华中科技大学科学研究基金资助

Eternal Solutions of the Boltzmann Equation

Wei Jinbo; Zhang Xianwen

Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074

Received:2004-09-20 Revised:2005-07-07 Online:2007-04-25 Published:2007-04-25
Contact: Wei Jinbo

摘要/Abstract

摘要： 该文讨论如下空间非均匀的Boltzmann方程
\frac{\partial f}{\partial t} + \xi\cdot \nabla_{x}f(t,x,\xi) = Q(f, f).
在角截断的硬位势情况下, 对初值接近行波Maxwell分布时,作者利用一种新的迭代方法, 证明了该方程存在一个非负的永久型解. 因此在空间区域无界的情形下,该文对Villani的猜测给出了否定的回答[12, 13].

关键词: Boltzmann方程, Kaniel-Shinbrot迭代, 永久型解

Abstract: In this paper, the authors discuss the following spatially inhomogeneous Boltzmann equation
\frac{\partial f}{\partial t} + \xi\cdot \nabla_{x}f(t, x, \xi) = Q(f, f).
By means of a new iteration method, the existence of a positive eternal solution with initial data close to a travelling Maxwellian is proved in the case of hard potentials with angular cut-off. Hence, the authors give a negative answer to the conjecture of Villani [12, 13] in the case of unbounded space domain.

Key words: Boltzmann equation, Kaniel-Shinbrot iteration, Eternal solution

中图分类号:

82C40

魏金波; 张显文. Boltzmann方程的永久型解[J]. 数学物理学报, 2007, 27(2): 240-247.

Wei Jinbo; Zhang Xianwen. Eternal Solutions of the Boltzmann Equation[J]. Acta mathematica scientia,Series A, 2007, 27(2): 240-247.

[1]	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.
[2]	姜正禄. 与相对论Boltzmann方程中的输运算子有关的紧性[J]. 数学物理学报, 1997, 17(3): 330-335.
[3]	陈建宁. Boltzmann方程的两个解的平均作为二粒子Boltzmann方程系的解[J]. 数学物理学报, 1990, 10(3): 259-272.