ON DECAY RATE OF QUENCHING PROFILE AT SPACE INFINITY FOR AXISYMMETRIC MEAN CURVATURE FLOW

被引：5

作者：

Giga, Yoshikazu ^{[1
]}

Seki, Yukihiro ^{[1
]}

Umeda, Noriaki ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 29卷 / 04期

基金：

日本学术振兴会;

关键词：

At space infinity; axisymmetric mean curvature flow equation; quenching profile; decay rate; LINEAR PARABOLIC EQUATIONS; SEMILINEAR HEAT-EQUATIONS; BLOW-UP;

D O I：

10.3934/dcds.2011.29.1463

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 is an element of R). We are interested to estimate its pro file 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) similar to vertical bar x vertical bar(-a) as vertical bar x vertical bar -> infinity if u (x, 0) tends to its infimum with algebraic rate vertical bar x vertical bar (2a)(as vertical bar x vertical bar -> infinity with a > 0).

引用

页码：1463 / 1470

页数：8

共 13 条

[1]

GIGA MH, 1999, PROGR NONLINEAR DIFF, V79

[2] On blow-up at space infinity for semilinear heat equations [J].