波茲曼方程解在邊界上的奇異行為

Abstract

十一、研究計畫中英文摘要：請就本計畫要點作一概述，並依本計畫性質自 訂關鍵詞。（一）計畫中文摘要。（五百字以內）

計畫在數學上刻劃波茲曼方程的解在邊界上各式的奇異行為。

第一年計畫借兩平板間的熱溢流問題研究邊界上微觀速度分布函數的不連續 性和二階對數奇異性。

第二年計畫研究巨觀變量梯度在平面邊界上的對數奇異性的一般性。並計畫 研究微觀速度分布函數的奇異性的一般性。

We propose to characterize mathematically various singular behavior of the solutions to Boltzmann equation on the boundary.

In the first year, we propose to study the jump discontinuity and secondary singularity of logarithmic type of the microscopic velocity distribution function on a planar boundary for thermal transpiration problem between two plates.

In the second year, we propose to study the logarithmic singularity of the gradient of macroscopic variables on a planar boundary under a general setting. Also, we propose to investigate the singular behavior of the microscopic velocity distribution function on a planar boundary for general problems.