Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (4): 958-969.

• Articles • Previous Articles     Next Articles

Existence of Weak Solutions for the Minimizing Total Variation Flow with Dirichlet Boundary Conditions

 RUI Jie, YANG Xiao-Ping   

  1. School of Mathematics and Computational Sciences, China University of Petroleum, Shandong Dongying 257061; School of Science, Nanjing University of Science and Technology, Nanjing 210094
  • Received:2009-07-09 Revised:2010-08-05 Online:2011-08-25 Published:2011-08-25

Abstract:

This paper concludes that the minimizing total variation flow with Dirichlet boundary conditions has a weak solution with initial data in L1(Ω) by using Crandall-Liggett's semigroup generation theorem and the quality of the completely accretive  operator.

Key words: Completely accretive operator, Mild solution, Strong solution, Weak solution

CLC Number: 

  • 47B44
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