On some classes of inverse problems for parabolic and elliptic equations
type: Item
instance of: scholarly article
title: On some classes of inverse problems for parabolic and elliptic equations
zbMATH Open document ID: 1239.35187
author: B. N. Tsybikov
author: S. G. Pyatkov
published in: Journal of Evolution Equations
publication date: 2012-01-13T00:00:00Z
review text: An inverse problem associated with parabolic and elliptic equations is considered. The authors study the solvability of such inverse problems of finding the solution together with some functions on the right-hand-side of the equation, when some supplementary conditions are given. These overdetermination conditions are represented by the values of a solution on some system of surfaces. Problems of this type arise in heat and mass transfer, diffusion and filtration processes. The authors prove that the considered parabolic problem is not always solvable, and they present solvability conditions. Moreover, they show that the problem is always solvable if the overdetermination condition is understood in some generalized sense.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35N20
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 5997667
zbMATH Keywords: parabolic equation
zbMATH Keywords: elliptic equation
zbMATH Keywords: inverse problem
zbMATH Keywords: control problem
zbMATH Keywords: heat and mass transfer
MaRDI profile type: Publication
full work available at URL: s00028-010-0087-6
OpenAlex ID: W2006122205
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DOI: 10.1007/S00028-010-0087-6
description: scientific article; zbMATH DE number 5997667