複合更新理論應用在散射邊界上

Abstract

研究的是具有散射邊界條件的漂移方程,此模型描述在上半空間裡一團接近真空的氣體。我們的工作得到了當時間趨近無窮的漸近結果。此外,研究了一些與微分方程的結構和邊界條件有關的隨機過程。漂移方程的顯式解是一個更新函數。局部極限定理是我們研究此函數的主要工具。我們問題中它有更多結構,因此,這個漸進結果在不同的時空關係下由第二速率函數的額外屬性所決定。

A transport equation with a diffuse boundary condition is studied for the propagation of a gas near vacuum. Our work reaches an large time asymptotic results. Also, some stochastic processes concerning the structure of the differential equation and the boundary condition were studied. The characteristic method leads to the explicit solution of the transport quation, which is a renewal function. The local limit theorem is our main tool studying this function. When turning to the specific renewal function in our problem, more structures were revealed and the space-time relationship is given by extra properties of the second rate function.