The physisorbate-layer problem arising in kinetic theory of gas-surface interaction. (English) Zbl 07845545
The study considers a half-space problem for a linear kinetic equation describing gas molecules that are physisorbed near a solid surface, relevant to kinetic models of gas-surface interactions as derived by K. Aoki et al. [Phys. Rev. E, 106, No. 3, Article ID 035306, 25 p. (2022; doi:10.1103/PhysRevE.106.035306)]. The equation incorporates a confinement potential near the solid surface and an interaction term between gas molecules and phonons. It is shown that a unique solution exists when the incoming molecular flux is specified at infinity, thereby confirming that the half-space problem functions are suitable as the boundary condition for the Boltzmann equation. Additionally, it is demonstrated that the sequence of approximate solutions used in the proof of existence converges exponentially fast. Numerical results detailing the solution to the half-space problem are also provided.
Reviewer: Lingda Xu (Hong Kong)
MSC:
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 35Q20 | Boltzmann equations |
| 82B40 | Kinetic theory of gases in equilibrium statistical mechanics |
Keywords:
Boltzmann equation; boundary condition; physisorbed molecule; existence; uniqueness; iterative approximate solution; exponential convergenceReferences:
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