Calculus of Variations and Partial Differential Equations

, Volume 34, Issue 2, pp 153–178

Expanding convex immersed closed plane curves

Article

DOI: 10.1007/s00526-008-0180-7

Cite this article as:
Lin, TC., Poon, CC. & Tsai, DH. Calc. Var. (2009) 34: 153. doi:10.1007/s00526-008-0180-7

Abstract

We study the evolution driven by curvature of a given convex immersed closed plane curve. We show that it will converge to a self-similar solution eventually. This self-similar solution may or may not contain singularities. In case it does, we also have estimate on the curvature blow-up rate.

Mathematics Subject Classification (2000)

35K1535K55

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsNational Taiwan UniversityTaipeiTaiwan
  2. 2.Department of MathematicsNational Chung Cheng UniversityChiayiTaiwan
  3. 3.Department of MathematicsNational Tsing Hua UniversityHsinchuTaiwan