Movement of hot spots over unbounded domains in \({\mathbb{R}}^ N\)
type: Item
instance of: scholarly article
title: Movement of hot spots over unbounded domains in \({\mathbb{R}}^ N\)
zbMATH Open document ID: 0830.35046
author: Shuichi Jimbo
author: Shigeru Sakaguchi
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-06-08T00:00:00Z
review text: The authors study the heat equation a) on a half space \(\mathbb{R}^+_n\), b) on the exterior of a ball with radial initial data, c) on the exterior of a bounded set \(\Omega\), and investigate the location and movement of hot spots for large \(t\) and under boundary conditions of Dirichlet, Neumann and Robin type. In the half plane case and for Neumann boundary conditions, for instance, the hot spot moves to the boundary in finite time, which (partially) answers a conjecture of J. Rauch. This and other results are shown by the moving plane method. In case b) one has \(r\) as a single space variable and one can use lap-number arguments to show that the set of hot spots becomes a single sphere after finite time. For the situation c) the results are less specific.
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 584092
zbMATH Keywords: movement of hot spots
zbMATH Keywords: moving plane method
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1123
OpenAlex ID: W2093401591
DOI: 10.1006/JMAA.1994.1123
description: scientific article; zbMATH DE number 584092