半空间中具有反射边界的线性玻尔兹曼模型的分数扩散极限

IF 1 4区数学 Q1 MATHEMATICS Kinetic and Related Models Pub Date : 2023-01-01 DOI:10.3934/krm.2023033

Ludovic Cesbron

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引用次数: 3

摘要

研究了具有麦克斯韦边界条件的半空间中具有重尾速度平衡的线性玻尔兹曼方程的分数扩散极限。我们在空间有界区域上导出了分数阶拉普拉斯算子的一个新的受限形式，并证明了相关非局部扩散方程弱解的唯一性。

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Fractional diffusion limit of a linear Boltzmann model with reflective boundaries in a half-space

We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian in a spatially bounded domain and show uniqueness of weak solution to the associated non-local diffusion equation.

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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.