总能量守恒下稀薄气体的热化：存在性、亚强制性与宏观极限
Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit
AI总结：
针对动能与背景热耦合的非线性弛豫系统，证明一维环面解的存在性、任意维环面平衡态谱稳定，并形式导出非线性交叉扩散宏观极限。
摘要：
气体向具有背景温度的 Maxwell 速度分布的热化由一个动力学弛豫模型描述。气体动能与背景热能之和守恒，而背景中的热流受 Fourier 定律支配。对于动力学方程与热方程构成的耦合非线性系统，本文在一维环面上证明了解的存在性。借助亚强制性方法，在任意维数的环面上证明了平衡态的谱稳定性。此外，还形式化地完成了向一个非线性交叉扩散问题的宏观极限。
英文摘要：
The thermalization of a gas towards a Maxwellian velocity distribution with the background temperature is described by a kinetic relaxation model. The sum of the kinetic energy of the gas and the thermal energy of the background are conserved, and the heat flow in the background is governed by the Fourier law. For the coupled nonlinear system of the kinetic and the heat equation, existence of solutions is proved on the one-dimensional torus. Spectral stability of the equilibrium is shown on the torus in arbitrary dimensions by hypocoercivity methods. The macroscopic limit towards a nonlinear cross-diffusion problem is carried out formally.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
