退化 SDE 的熵估计及其在非线性动力学福克-普朗克方程中的应用

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-19 DOI:10.1137/24m1634473

Zhongmin Qian, Panpan Ren, Feng-Yu Wang

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷第 4 期，第 5330-5349 页，2024 年 8 月。摘要。利用初始分布的瓦瑟斯坦距离和系数差估算两种不同退化扩散过程的相对熵。作为应用，推导了与非线性动力学福克-普朗克方程相关的分布依赖性随机哈密顿系统的熵-代价不等式和熵的指数遍历性。

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Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker–Planck Equations

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5330-5349, August 2024.
Abstract. The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy-cost inequality and exponential ergodicity in entropy are derived for distribution dependent stochastic Hamiltonian systems associated with nonlinear kinetic Fokker–Planck equations.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.