具有重尾平衡的Fokker-Planck方程的分数扩散:任意维的 la Koch谱方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-24 DOI:10.3233/asy-231870

Dahmane Dechicha, Marjolaine Puel

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引用次数: 0

摘要

在本文中，我们将开发的频谱方法(Dechicha和Puel(2023))扩展到任何维度d大于或等于1，以便为具有重尾平衡的Fokker-Planck算子构建一个特征解，形式为(1 + | v | 2)−β 2，在β∈]d, d + 4[。在维1中开发的方法受到H. Koch关于非线性KdV方程(非线性28(2015)545)的工作的启发。本文中的策略与维度1中的相同，但工具不同，因为维度1是基于ODE方法的。作为我们构造的直接结果，我们得到了动力学Fokker-Planck方程的分数扩散极限，对于正确的密度ρ: =∫R d f d v，具有分数阶拉普拉斯算子κ(−Δ) β - d + 26和正扩散系数κ。

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Fractional diffusion for Fokker–Planck equation with heavy tail equilibrium: An à la Koch spectral method in any dimension

In this paper, we extend the spectral method developed (Dechicha and Puel (2023)) to any dimension d ⩾ 1, in order to construct an eigen-solution for the Fokker–Planck operator with heavy tail equilibria, of the form ( 1 + | v | 2 ) − β 2 , in the range β ∈ ] d , d + 4 [. The method developed in dimension 1 was inspired by the work of H. Koch on nonlinear KdV equation (Nonlinearity 28 (2015) 545). The strategy in this paper is the same as in dimension 1 but the tools are different, since dimension 1 was based on ODE methods. As a direct consequence of our construction, we obtain the fractional diffusion limit for the kinetic Fokker–Planck equation, for the correct density ρ : = ∫ R d f d v, with a fractional Laplacian κ ( − Δ ) β − d + 2 6 and a positive diffusion coefficient κ.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.