Kazuo Aoki, Vincent Giovangigli, François Golse, Shingo Kosuge
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引用次数: 0
摘要
研究考虑了气体分子物理吸附在固体表面附近的线性动力学方程的半空间问题,该方程与 Aoki 等人推导的气表相互作用动力学模型有关(Phys. Rev. E 106:035306, 2022)。该方程包含固体表面附近的约束势和气体分子与声子之间的相互作用项。研究证明,当输入的分子通量指定为无穷大时,存在一个唯一的解。这验证了半空间问题作为玻尔兹曼方程边界条件的自然观察结果。同时还证明,用于证明存在性的近似解序列以指数级速度收敛。此外,还给出了显示半空间问题求解细节的数值结果。
The Physisorbate-Layer Problem Arising in Kinetic Theory of Gas–Surface Interaction
A half-space problem of a linear kinetic equation for gas molecules physisorbed close to a solid surface, relevant to a kinetic model of gas–surface interaction and derived by Aoki et al. (Phys. Rev. E 106:035306, 2022), is considered. The equation contains a confinement potential in the vicinity of the solid surface and an interaction term between gas molecules and phonons. It is proved that a unique solution exists when the incoming molecular flux is specified at infinity. This validates the natural observation that the half-space problem serves as the boundary condition for the Boltzmann equation. It is also proved that the sequence of approximate solutions used for the existence proof converges exponentially fast. In addition, numerical results showing the details of the solution to the half-space problem are presented.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.