On heat conductors with a stationary hot spot

被引：11

作者：

Magnanini, Rolando ^{[1
]}

Sakaguchi, Shigeru ^{[2
]}

机构：

[1] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy

[2] Ehime Univ, Fac Sci, Dept Math Sci, Matsuyama, Ehime 7908577, Japan

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2004年 / 183卷 / 01期

基金：

日本学术振兴会;

关键词：

heat equation; convex bodies; hot spots; stationary critical point;

D O I：

10.1007/s10231-003-0077-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a heat conductor having initial constant temperature and zero boundary temperature at every time. The hot spot is the point at which temperature attains its maximum at each given time. For convex conductors, if the hot spot does not move in time, we prove symmetry results for planar triangular and quadrangular conductors. Then, we examine the case of a general conductor and, by an asymptotic formula, we prove that, if there is a stationary critical point, not necessarily the hot spot, then the conductor must satisfy a geometric condition. In particular, we show that there is no stationary critical point inside planar non-convex quadrangular conductors.

引用

页码：1 / 23

页数：23