### Movement of hot spots on the exterior domain of a ball under the Dirichlet boundary condition

Kazuhiro Ishige

#### Abstract

We consider the Cauchy-Dirichlet problem of the heat equation in the exterior domain of a ball, and study the movement of hot spots $H(t)$ as $t\to\infty$. In particular, we give a rate for the hot spots to run away from the boundary of the domain as $t\to\infty$. Furthermore we give a sufficient condition for the hot spots to consist of only one point after a finite time.

#### Article information

Source
Adv. Differential Equations, Volume 12, Number 10 (2007), 1135-1166.

Dates
First available in Project Euclid: 29 April 2013

Mathematical Reviews number (MathSciNet)
MR2362266

Zentralblatt MATH identifier
1152.35321

Subjects
Primary: 35K05: Heat equation
Secondary: 35B40: Asymptotic behavior of solutions

#### Citation

Ishige, Kazuhiro. Movement of hot spots on the exterior domain of a ball under the Dirichlet boundary condition. Adv. Differential Equations 12 (2007), no. 10, 1135--1166. https://projecteuclid.org/euclid.ade/1367241161