On a certain inverse problem for the heat equation on the circle
type: Item
instance of: scholarly article
title: On a certain inverse problem for the heat equation on the circle
zbMATH Open document ID: 0538.35076
author: Takashi Suzuki
published in: Proceedings of the Japan Academy. Series A
publication date: 1982-01-01T00:00:00Z
review text: This is one of a series of papers by the present author and by others, dealing with the problem of determining the potential q(x) or the potential as well as the initial value u(x,0), in the parabolic equation \(u_ t-u_{xx}+q(x)u=0\). To achieve this, one typically gives some combination of overposed data on characteristic lines. The present paper is concerned with periodic boundary conditions in the space variable and the complicating factor here is the possibility of double eigenvalues. Necessary conditions are given for uniquely determining the potential and the initial data when the values of \(u(x_ i,t)\) and of \(u_ x(x_ i,t)\) are prescribed for various choices of the points \(x_ i\). The proofs will be found in a forthcoming paper.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3855625
zbMATH Keywords: undetermined coefficients
zbMATH Keywords: periodic potential
zbMATH Keywords: periodic boundary conditions
MaRDI profile type: Publication
full work available at URL: pjaa.58.243
OpenAlex ID: W2094587976
cites work: Q3944981
cites work: Uniqueness and nonuniqueness in an inverse problem for the parabolic equation
cites work: Remarks on the uniqueness in an inverse problem for the heat equation. I
cites work: Remarks on the uniqueness in an inverse problem for the heat equation. II
cites work: A uniqueness theorem in an identification problem for coefficients of parabolic equations
DOI: 10.3792/PJAA.58.243
description: scientific article; zbMATH DE number 3855625