On decay rate of quenching profile at space infinity for axisymmetric mean curvature flow

Yoshikazu Giga, Yukihiro Seki, Noriaki Umeda

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study the motion of noncompact hypersurfaces moved by their mean curvature obtained by a rotation around x-axis of the graph a function y = u(x, t) (defined for all x ∈ R). We are interested to estimate its profile when the hypersurface closes open ends at the quenching (pinching) time T. We estimate its profile at the quenching time from above and below. We in particular prove that u(x, T)∼ |x|→aas |x| → ∞ if u(x, 0) tends to its infimum with algebraic rate |x|-2a (as |x| → ∞ with a > 0).

Original languageEnglish
Pages (from-to)1463-1470
Number of pages8
JournalDiscrete and Continuous Dynamical Systems
Volume29
Issue number4
DOIs
Publication statusPublished - Apr 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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