具非线性梯度源和奇异势的快扩散方程解的熄灭

刘灯明; 丁一格; 杨吉晨

doi:10.1051/wujns/2026315437

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具非线性梯度源和奇异势的快扩散方程解的熄灭

Mathematics | 更新时间：2026-10-29

- 具非线性梯度源和奇异势的快扩散方程解的熄灭
- Extinction for a Fast Diffusion Equation Involving a Nonlinear Gradient Source and a Singular Potential
- 武汉大学学报自然科学英文版 2026年31卷第5期页码：437-442
- 作者机构：
  
  湖南科技大学数学与统计学院，湖南湘潭 411201
- 作者简介：
  
  LIU Dengming, male, Ph. D., Professor, research direction: nonlinear partial differential equations. E-mail: liudengming@hnust.edu.cn
- 基金信息：
  
  Scientific Research Fund of Hunan Provincial Education Department(23A0361)
- DOI：10.1051/wujns/2026315437
  中图分类号： O175.29
- 收稿：2026-03-27，
  
  纸质出版：2026-10-24
- 稿件说明：
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刘灯明,丁一格,杨吉晨.具非线性梯度源和奇异势的快扩散方程解的熄灭[J].武汉大学学报自然科学英文版,2026,31(05):437-442.

LIU Dengming, DING Yige, YANG Jichen. Extinction for a Fast Diffusion Equation Involving a Nonlinear Gradient Source and a Singular Potential[J]. Wuhan Univ J of Nat Sci, 2026, 31(5): 437-442.
刘灯明,丁一格,杨吉晨.具非线性梯度源和奇异势的快扩散方程解的熄灭[J].武汉大学学报自然科学英文版,2026,31(05):437-442. DOI： 10.1051/wujns/2026315437.

LIU Dengming, DING Yige, YANG Jichen. Extinction for a Fast Diffusion Equation Involving a Nonlinear Gradient Source and a Singular Potential[J]. Wuhan Univ J of Nat Sci, 2026, 31(5): 437-442. DOI： 10.1051/wujns/2026315437.

摘要

本文研究了含非线性梯度源与奇异势项的快扩散方程解的熄灭行为。利用能量估计方法、Hardy-Littlewood-Sobolev不等式和微分不等式技巧，给出了一类具非线性梯度源和奇异势的快扩散方程解在有限时刻发生熄灭现象的充分条件。同时，利用上、下解方法，证明了非熄灭解的存在性。

Abstract

This article deals with the extinction behavior of the solution for a fast diffusion equation involving a nonlinear gradient source and a singular potential. Based on the energy estimate method

the Hardy-Littlewood-Sobolev inequality

and the ordinary differential inequality approach

we obtain the sufficient conditions on the occurrence of the finite time extinction phenomenon of the weak solution. Meanwhile

we establish the existence of a non-extinction weak solution via constructing suitable non-extinction sub- and super-solutions and applying the standard iteration process.

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references

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