Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (1): 157-164.

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

Tianling Gao1,Li Xia2,*(),Mingjun Zhou3,Yuanyuan Zhang4   

  1. 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)

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

CLC Number: 

  • O29
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