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Effect of Abrupt Change of the Wall Temperature in the Kinetic Theory

Speaker

Hung-Wen Kuo, National Cheng Kung University

Time

2018.10.12 10:00-11:00

Venue

601,Pao Yue-Kong Library

Abstract

Consider a semi-infinite expanse of a rarefied gas bounded by an infinite plane wall. We study the quantitative short time behavior of the gas in response to the abrupt change of the wall temperature on the basis of the linearized Boltzmann equation. Our approach is based on a straightforward calculation of the exact formulas derived by Duhamel’s integral. Our method allows us to establish the pointwise estimates of the microscopic distribution and the macroscopic variables in short time. We show that the short-time solution consists of the free molecular flow and its perturbation, which exhibits logarithmic singularities along the characteristic line and on the boundary.