论文标题
具有总能量的稀有气体的热化：存在，低脑，宏观极限
Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit
论文作者
论文摘要
气体朝着具有背景温度的麦克斯韦速度分布的热量通过动力学弛豫模型描述。气体的动能和背景的热能的总和是保守的，背景中的热流受傅立叶定律的控制。 对于动力学和热方程的耦合非线性系统，在一维圆环上证明了溶液的存在。平衡的频谱稳定性通过低脑性方法在任意维度上显示在圆环上。对非线性交叉扩散问题的宏观极限是正式实现的。
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.
