具非定常数初值的全变差方程解的渐近性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 157-164.

具非定常数初值的全变差方程解的渐近性

高天玲¹,夏莉^2,*(),周鸣君³,张园园⁴

¹ 深圳大学数学与统计学院广东深圳 518060
² 广东财经大学统计与数学学院广州 510320
³ 吉林大学数学系长春 130012
⁴ 西南财经大学证券与期货学院成都 611130

收稿日期:2019-03-20 出版日期:2022-02-26 发布日期:2022-02-23
通讯作者: 夏莉 E-mail:xaleysherry@163.com
基金资助:
国家自然科学基金(11571137);广东省自然科学基金(2015A030313623);广东省自然科学基金(2016A030313048)

The Asymptotic Behavior of Total Variation Flow with the Non-Constant Data

Tianling Gao¹,Li Xia^2,*(),Mingjun Zhou³,Yuanyuan Zhang⁴

¹ College of Mathematics and Statistics, Shenzhen University, Guandong Shenzhen 518060
² College of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320
³ School of Mathematics, Jilin University, Changchun 130012
⁴ School of Securities and Futures, Southwestern University of Finance and Economics, Chengdu 611130

Received:2019-03-20 Online:2022-02-26 Published:2022-02-23
Contact: Li Xia E-mail:xaleysherry@163.com
Supported by:
the NSFC(11571137);the NSF of Guangdong Province(2015A030313623);the NSF of Guangdong Province(2016A030313048)

摘要/Abstract

摘要：

该文主要研究具有非定常数初值的全变差方程解的渐近性，证明了：当参数λ小于某个临界值时，解在有限时间内收敛到一个常数；当参数λ大于某个临界值时，如果初值不是常数，则解在有限时间内一定不收敛到常数.

关键词: 渐近性, 全变差方程, 非常数初值

Abstract:

In this paper, we study the asymptotic behavior for the total variation flow with the non-constant data. We prove that when the tuning parameter λ is less than some critical value, the solution will converge to a constant in a finite time, and when the tuning parameter λ is larger than the critical value, the solution does not converge to any constant in finite time if the initial data is not a constant.

Key words: Asymptotic behavior, Total variation flow, Non-constant data

中图分类号:

高天玲,夏莉,周鸣君,张园园. 具非定常数初值的全变差方程解的渐近性[J]. 数学物理学报, 2022, 42(1): 157-164.

Tianling Gao,Li Xia,Mingjun Zhou,Yuanyuan Zhang. The Asymptotic Behavior of Total Variation Flow with the Non-Constant Data[J]. Acta mathematica scientia,Series A, 2022, 42(1): 157-164.

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