一类限流扩散方程及其 $BV$ 理论进展——献给陈化教授 70 寿辰

数学物理学报 ›› 2026, Vol. 46 ›› Issue (2): 604-615.

一类限流扩散方程及其 $BV$ 理论进展——献给陈化教授 70 寿辰

罗永¹(), 王春朋¹(), 尹景学¹^,²^,^*()

¹ 吉林大学数学学院长春 130012
² 华南师范大学数学科学学院广州 510631

收稿日期:2025-12-19 修回日期:2025-01-04 出版日期:2026-04-26 发布日期:2026-04-27
通讯作者: 尹景学 E-mail:wangcp@jlu.edu.cn;yjx@scnu.edu.cn
作者简介:罗永, Email：wangcp@jlu.edu.cn
王春朋, Email：wangcp@jlu.edu.cn

Flux-Limited Diffusion Equations and Their $BV$ Theory

Yong Luo¹(), Chunpeng Wang¹(), Jingxue Yin¹^,²^,^*()

¹ School of Mathematics, Jilin University, Changchun 130012
² School of Mathematical Sciences, South China Normal University, Guangzhou 510631

Received:2025-12-19 Revised:2025-01-04 Online:2026-04-26 Published:2026-04-27
Contact: Jingxue Yin E-mail:wangcp@jlu.edu.cn;yjx@scnu.edu.cn

摘要/Abstract

摘要：

该文简要回顾了一类限流扩散模型 $BV$ 熵解的基本理论进展, 包括熵解定义与适定性、双曲特征与熵条件以及有限传播等核心性质. 旨在为后续关于大梯度退化的非线性抛物方程的研究提供已有基本框架与主要发展脉络的综述.

关键词: 限流扩散, $BV$ 熵解, 双曲特征, 有限传播

Abstract:

We briefly review the $BV$ entropy theory for a class of flux-limited diffusion equations, including the notion and well-posedness of entropy solutions, the hyperbolic features and entropy conditions, and the finite speed of propagation. The purpose is to serve as a basic theoretical framework for subsequent investigations of nonlinear parabolic equations exhibiting large-gradient degeneracy.

Key words: flux-limited diffusion, $BV$ entropy solution, hyperbolic features, finite propagation

中图分类号:

O175.29

罗永, 王春朋, 尹景学. 一类限流扩散方程及其 $BV$ 理论进展——献给陈化教授 70 寿辰[J]. 数学物理学报, 2026, 46(2): 604-615.

Yong Luo, Chunpeng Wang, Jingxue Yin. Flux-Limited Diffusion Equations and Their $BV$ Theory[J]. Acta mathematica scientia,Series A, 2026, 46(2): 604-615.

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