| 均匀格子气Boltzmann方程的稳定性研究 |
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| 引用本文： | 孙成海,史俊杰.均匀格子气Boltzmann方程的稳定性研究[J].计算数学,2000,22(1):1-12. |
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| 作者姓名： | 孙成海 史俊杰 |
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| 作者单位： | 1. 清华大学工程力学系,北京,100084
2. 清华大学图书馆,北京,100084 |
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| 基金项目： | 国家自然科学基金!（批准号 19672030和 19972037），国家教委留学回国人员经费资助 |
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| 摘 要： | １．引言格子气的基本方程是在几何空间、速度空间和时间上都是离散的Ｂｏｌｔｚｍａｎｎ方程（Ｂ方程）．这是一个有限差分方程．在离散速度气体运动论中［１］，Ｂ方程在速度空间上是离散的，在几何空间和时间上是连续的．这是一个偏微分方程．人们对离散速度气体Ｂ方程的稳定性和渐近特性的研究已经取得了很多结果．Ｍａａｓｓ~［２］通过构造Ｌｙaｐｕｎｏｖ函数族，在分布函数在空间上均匀的条件下，证明了平衡分布的渐近稳定性．信息函数Ｈ是该函数族的一员．Ｂｅｌｌｏｍｏｅｔａｌ~［３］．采用小扰动线性化方法在初值距离平衡解足…
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| 关 键 词： | 格子气 Lyapunov函数 稳定性 Boltzmann方程 |
STUDY OF THE STABILITY OF THE HOMOGENEOUS BOLTZMANN EQU ATION FOR LATTICE GASES |
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| Sun Chenghai,Shi Junjie.STUDY OF THE STABILITY OF THE HOMOGENEOUS BOLTZMANN EQU ATION FOR LATTICE GASES[J].Mathematica Numerica Sinica,2000,22(1):1-12. |
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| Authors: | Sun Chenghai Shi Junjie |
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| Institution: | Sun Chenghai (Department of Engineering Mechanics, Tsinghua University, Beijing, 100084) Shi Junjie (Tsinghua University Library Beijing, 100084) |
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| Abstract: | The Lyapunov method is applied to finite difference equations in order to study the stability and asymptotic properties of Boltzmann equation of lattice gas. The existence and uniqueness of the equilibrium state are proved. A Lyapunov function can be formed by means of function H that is decreasing and takes its minimum value at the equilibrium state. By the Lyapunov function the stability is Obtained. Moreover, a sufficient condition is provided that makes the function H strictly decrease except at the equilibrium state. The asymptotic stability for homogeneous Boltzmann equation of lattice gas is proved under this condition. |
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| Keywords: | Lattice gas Lyapunov function stability |
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