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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Mathematical Sciences. The University of Tokyo
( Vol. 3 NO.1 / (1996))
The Heat Flows of Harmonic Maps from $S^2$ to $S^2$
Keisui Asai,
Pages. 1-13
Abstract In this paper we show that the heat flow $u(x,t)$ with a rotationally symmetric
initial map $u_0 (x,t)$ converges to a harmonic map as $t to infty$ if $n=1$
and $0<h(theta)<pi (theta in (0,pi))$. Here we call $u_0: S^2 to S^2$
rotationally symmetric if there exists a function $h:[0,pi] to R$ such that
$h(0) =0, ; h(pi)= n pi$, and $u(cos tau sin theta, sin tau sin
theta cos theta)= (cos tau sin h(theta), sin tau sin h(theta), cos
h(theta))$.
Contents 0. Introduction
1. The heat flows of the harmonic maps
2. Solutions with rotationally symmetric initial maps
3. The proof of theorem
Key words
Mathmatical Subject Classification 58E20