The narrow escape problem -- a short review of recent results
type: Item
instance of: scholarly article
title: The narrow escape problem -- a short review of recent results
zbMATH Open document ID: 1259.82083
published in: Journal of Scientific Computing
publication date: 2013-01-10T00:00:00Z
review text: The mean first passage time or narrow escape time of a particle from a point \(x\) in a bounded domain to the absorbing boundary is understood as being the mean of the solution of a mixed Dirichlet-Neumann boundary value problem for the Poisson equation. The Narrow Escape Problem (NET) consists of calculating this mean. In the literature, contributions on three main classes of this NET problem are known: absorbing patches on a smooth boundary (class1), absorbing patches at the end of a smooth funnel (class2), patches at the end of a long narrow neck attached smoothly or non-smoothly to the reflecting boundary (class3). In the present article, one reviews -- shortly -- some recent results for domains of these classes, in two as well in as in three dimensions. To this very short paper, references of 41 titles are attached.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 82C32
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 6123937
zbMATH Keywords: Brownian motion
zbMATH Keywords: mean first passage time
zbMATH Keywords: singular perturbations
zbMATH Keywords: Poisson equation
zbMATH Keywords: Dirichlet-Neumann boundary value problem
author: Zeev Schuss
MaRDI profile type: Publication
full work available at URL: s10915-012-9590-y
OpenAlex ID: W1983932366
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DOI: 10.1007/S10915-012-9590-Y
description: scientific article; zbMATH DE number 6123937