Science in China Series A: Mathematics

, Volume 52, Issue 10, pp 2177–2184 | Cite as

A curve flow evolved by a fourth order parabolic equation

Article
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Abstract

We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ℝ2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.

Keywords

geometric evolution equations fourth order energy estimate 

MSC(2000)

35J60 35K45 52K44 53A05 
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Copyright information

© Science in China Press and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.School of computer science and information engineeringBeijing Technology and Business UniversityBeijingChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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