An inverse heat equation in two space dimensions.
type: Item
instance of: scholarly article
title: An inverse heat equation in two space dimensions.
zbMATH Open document ID: 1072.35200
published in: Applied Mathematics Letters
publication date: 2005-03-07T00:00:00Z
review text: The author generalizes a result of [\textit{A. G. Ramm}, Proc. R. Soc. Edinb., Sect. A 123, No. 6, 973--976 (1993; Zbl 0804.35153)], to the two-dimensional case. The argument is applicable to the multidimensional case as well. The following inverse problem is studied: Consider a bounded domain \(D\) with a sufficiently smooth boundary \(S\), \(D=D_1\cup D_2\), and denote by \(\Gamma\) the sufficiently smooth surface, which is the common part of the boundary of \(D_1\) and \(D_2\). Let \(u_t=\nabla (a(x)\nabla u)\) in \(D\), \(u(x,0)=f(x)\), \(u=0\) on \(\partial D_1\setminus \Gamma\), \(u=g\) on \(\Gamma\). Denote \(\psi:=u\) on \(\partial D_2\setminus \Gamma\). Assume that \(a\) is strictly positive and sufficiently smooth, say \(C^1\). The inverse problem consists of finding \(\psi\) given \(a,f,\) and \(g\). The author proves that this problem has at most one solution.
reviewed by: A. G. Ramm
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 2140798
zbMATH Keywords: heat equation
zbMATH Keywords: inverse problem
zbMATH Keywords: uniqueness
zbMATH Keywords: unique continuation
author: Behrouz Emamizadeh
MaRDI profile type: Publication
full work available at URL: j.aml.2003.09.009
OpenAlex ID: W1966914720
cites work: An inverse problem for the heat equation
cites work: Q4023365
cites work: Q4693168
cites work: Unique continuation for some evolution equations
cites work: Q5562267
DOI: 10.1016/J.AML.2003.09.009
description: scientific article; zbMATH DE number 2140798