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 $0<π$ $(θ\in(0,π))$. Here we call $u_0:S^2 \to S^2$ rotationally symmetric if there exists a function $h:[0,π] \to R$ such that $h(0)=0,$ $h(π)=nπ,$ and $u(\cosτ\sinθ,\sinτ\sinθ,\cosθ) =(\cosτ\sin h(θ),\sinτ\sin h(θ),\cos h(θ)).$
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
3
号
1
ページ
1 - 13
発行年
1996
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1414616
Mathmatical Subject Classification
58E20(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
The Heat Flows of Harmonic Maps from $S^2$ to $S^2$
jms030101.pdf
(121.49KB)
