Inverse problems of the determination of the coefficient in parabolic equations. I
type: Item
instance of: scholarly article
title: Inverse problems of the determination of the coefficient in parabolic equations. I
zbMATH Open document ID: 0784.35122
DOI: 10.1007/BF00970897
author: A. B. Kostin
author: Aleksey Ivanovic Prilepko
published in: Siberian Mathematical Journal
publication date: 1993-03-18T00:00:00Z
review text: The authors prove uniqueness theorems for the determination of \(c(x)\) in the equation \[ u_ t-Lu=cu+g \] resp. the determination of \(\rho(x)\) in the equation \[ \rho u_ t-Lu=g \] on \(\Omega \times (0,T)\), \(\Omega\) a bounded domain in \(\mathbb{R}^ n\), \(L\) an elliptic operator of the second order. Besides, an initial condition, a boundary condition on \(\partial \Omega \times [0,T]\) of Dirichlet type or type \(\partial u/ \partial \nu+\sigma(x)u\), and additionally \(u(x,t_ 1)\) for \(x \in \Omega\) and a fixed \(t_ 1\), \(0<t_ 1 \leq T\), or \(\int^ T_ 0u(x,\tau) \omega(\tau)d \tau\) are given.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 130813
zbMATH Keywords: inverse problems
zbMATH Keywords: uniqueness theorems
zbMATH Keywords: bounded domain
reviewed by: Gottfried Bruckner
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00970897
OpenAlex ID: W2034502663
description: scientific article; zbMATH DE number 130813