圆盘自由输运方程的$ C^{2} $解

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2021-12-03 DOI:10.3934/krm.2022031

G. Ko, Donghyung Lee

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引用次数: 3

摘要

The free transport operator of probability density function \begin{document}$ f(t, x, v) $\end{document} is one the most fundamental operator which is widely used in many areas of PDE theory including kinetic theory, in particular. When it comes to general boundary problems in kinetic theory, however, it is well-known that high order regularity is very hard to obtain in general. In this paper, we study the free transport equation in a disk with the specular reflection boundary condition. We obtain initial-boundary compatibility conditions for \begin{document}$ C^{1}_{t, x, v} $\end{document} and \begin{document}$ C^{2}_{t, x, v} $\end{document} regularity of the solution. We also provide regularity estimates.

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On $ C^{2} $ solution of the free-transport equation in a disk

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.