ncku-talk2024-05-28

Analysis Seminar

DATE 2024-05-28　16:10-17:00

PLACE 數學系館 3F會議室

SPEAKER Professor Kazuo Aoki（National Cheng Kung University, Tainan, Taiwan and Kyoto University, Kyoto, Japan）

TITLE Models of Boundary Conditions for the Boltzmann Equation Based on a Kinetic Model of Gas-Surface Interaction

ABSTRACT Boundary conditions for the Boltzmann equation are investigated on the basis of a kinetic model of gas-surface interaction. The model takes into account the interaction of gas molecules with the molecules forming the solid. The layer of interaction is assumed to be thinner than the mean free path of the gas molecules, and the solid molecules are in equilibrium. The asymptotic kinetic equation for the interaction layer (physisorbate layer), which forms a steady half-space problem, is derived and used to investigate boundary conditions for the Boltzmann equation that is valid outside the physisorbate layer. To be more specific, new models of the boundary condition are proposed on the basis of iterative solutions of the half-space problem and are assessed by the direct numerical analysis of the problem. In addition, some rigorous mathematical results for the half-space problem are presented. This is a joint work with Vincent Giovangigli, Fran?ois Golse (Ecole Polytechnique) and Shingo Kosuge (Kyoto University).

Analysis Seminar

DATE	2024-05-28　16:10-17:00

PLACE	數學系館 3F會議室

SPEAKER	Professor Kazuo Aoki（National Cheng Kung University, Tainan, Taiwan and Kyoto University, Kyoto, Japan）

TITLE	Models of Boundary Conditions for the Boltzmann Equation Based on a Kinetic Model of Gas-Surface Interaction

ABSTRACT	Boundary conditions for the Boltzmann equation are investigated on the basis of a kinetic model of gas-surface interaction. The model takes into account the interaction of gas molecules with the molecules forming the solid. The layer of interaction is assumed to be thinner than the mean free path of the gas molecules, and the solid molecules are in equilibrium. The asymptotic kinetic equation for the interaction layer (physisorbate layer), which forms a steady half-space problem, is derived and used to investigate boundary conditions for the Boltzmann equation that is valid outside the physisorbate layer. To be more specific, new models of the boundary condition are proposed on the basis of iterative solutions of the half-space problem and are assessed by the direct numerical analysis of the problem. In addition, some rigorous mathematical results for the half-space problem are presented. This is a joint work with Vincent Giovangigli, Fran?ois Golse (Ecole Polytechnique) and Shingo Kosuge (Kyoto University).