Matzoh ball soup: Heat conductors with a stationary isothermic surface
type: Item
instance of: scholarly article
title: Matzoh ball soup: Heat conductors with a stationary isothermic surface
zbMATH Open document ID: 1011.35066
DOI: 10.2307/3597287
author: Rolando Magnanini
author: Shigeru Sakaguchi
published in: Annals of Mathematics. Second Series
publication date: 2003-03-24T00:00:00Z
full work available at URL: http://hdl.handle.net/2158/307188
review text: The main result of the paper is the following theorem: Let \(\Omega \) be a bounded domain in \(\mathbb{R}^N\), \(N\geq 2\), satisfying the exterior sphere condition and suppose that \(D\) is a domain, with boundary \(\partial D\), satisfying the interior cone condition, and such that \(\overline D\subset \Omega \). Let \(u\) be a solution of the problem \(u_t=\Delta u\) in \(\Omega \times (0,+\infty)\), \(u=1\) on \(\partial \Omega \times (0,+\infty)\), \(u=0\) on \(\Omega \times \{ 0\} \). Assume that \(u(x,t)=a(t)\) for \((x,t) \in \partial D \times (0,+\infty)\) for some function \(a:(0,+\infty) \to (0,+\infty)\). Then \(\Omega \) must be a ball.
reviewed by: Dagmar Medková
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B38
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1877087
zbMATH Keywords: stationary surfaces
MaRDI profile type: Publication
OpenAlex ID: W2031657962
description: scientific article; zbMATH DE number 1877087