Heat flow and Brownian motion for a region in \({\mathbb{R}}^ 2\) with a polygonal boundary
type: Item
instance of: scholarly article
title: Heat flow and Brownian motion for a region in \({\mathbb{R}}^ 2\) with a polygonal boundary
zbMATH Open document ID: 0682.60067
DOI: 10.1007/BF01207512
author: S. Srisatkunarajah
author: M. van den Berg
publication date: 1990-01-01T00:00:00Z
review text: Consider the following heat conduction problem. Let D be an open, bounded and connected set in Euclidean space \({\mathbb{R}}^ 2\) with a polygonal boundary. Suppose that D has temperature 1 at time \(t=0\), while the boundary is kept at temperature 0 for all time \(t>0\). We obtain the asymptotic behaviour for the amount of heat in D at time t up to \(O(e^{-q/t})\) as \(t\to 0\).
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 4117597
zbMATH Keywords: heat conduction problem
zbMATH Keywords: polygonal boundary
zbMATH Keywords: asymptotic behaviour
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4117597