A Half-space Problem for the Boltzmann Equation with Specular Reflection Boundary Condition
A Half-space Problem for the Boltzmann Equation with Specular Reflection Boundary Condition
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DOI：
10.1007/s00220-004-1278-1
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发表时间：
2005-02
影响因子：
2.4
通讯作者：
Tong Yang;Huijiang Zhao
中科院分区：
文献类型：
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作者：
Tong Yang;Huijiang Zhao
尽管气体动力学系统的稳定性理论已经比较完善，但Boltzmann方程的非线性波型的稳定性仍存在许多问题。本文研究了具有镜面反射边界效应的Boltzmann方程的稀疏波剖面在硬球模型和角截断硬势模型下的非线性稳定性。分析是基于解及其导数的性质，这些导数在边界处是来自镜面反射的奇函数或偶函数，以及解和Boltzmann方程在[24，26]中引入的能量方法的分解。
There are many open problems on the stability of nonlinear wave patterns to the Boltzmann equation even though the corresponding stability theory has been comparatively well-established for the gas dynamical systems. In this paper, we study the nonlinear stability of a rarefaction wave profile to the Boltzmann equation with the boundary effect imposed by specular reflection for both the hard sphere model and the hard potential model with angular cut-off. The analysis is based on the property of the solution and its derivatives which are either odd or even functions at the boundary coming from specular reflection, and the decomposition on both the solution and the Boltzmann equation introduced in [24, 26] for energy method.