TY - JOUR

T1 - On decay rate of quenching profile at space infinity for axisymmetric mean curvature flow

AU - Giga, Yoshikazu

AU - Seki, Yukihiro

AU - Umeda, Noriaki

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/4

Y1 - 2011/4

N2 - 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).

AB - 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).

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U2 - 10.3934/dcds.2011.29.1463

DO - 10.3934/dcds.2011.29.1463

M3 - Article

AN - SCOPUS:79954503146

VL - 29

SP - 1463

EP - 1470

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 4

ER -