总能量守恒的稀薄气体的热化:存在、低矫顽力、宏观极限

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2020-12-14 DOI:10.3934/krm.2022015

Gianluca Favre, M. Pirner, C. Schmeiser

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引用次数: 3

摘要

用动力学松弛模型描述了气体随背景温度向麦克斯韦速度分布的热化过程。气体的动能和背景的热能之和守恒，背景中的热流服从傅里叶定律。对于动力学方程和热方程耦合的非线性系统，在一维环面上证明了解的存在性。用准矫顽力方法证明了平衡态在环面任意维度上的谱稳定性。给出了非线性交叉扩散问题的宏观极限。

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Thermalization of a rarefied gas with total energy conservation: Existence, hypocoercivity, macroscopic limit

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.

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.