Reduction of multidimensional inverse problems to initial-boundary value problems in Hilbert spaces
type: Item
instance of: scholarly article
title: Reduction of multidimensional inverse problems to initial-boundary value problems in Hilbert spaces
zbMATH Open document ID: 0866.35133
DOI: 10.1007/BF02104808
author: Yu. E. Anikonov
author: Mikhail P. Vishnevskii
published in: Siberian Mathematical Journal
publication date: 1997-07-24T00:00:00Z
review text: A nonlinear multidimensional inverse problem for an evolution equation of a general type is considered. The problem under consideration can be reduced to two problems with initial data for evolution equations in a Hilbert space. One of the transformed problems is nonlinear, the other linear. Since the initial data for the transformed problems are uniquely determined by the information that is given in the inverse problem, this allows constructing solutions of the inverse problem by the proposed approach. In some case, explicit formulae for a solution to the inverse problem can be written down.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 917060
zbMATH Keywords: multidimensional inverse problem
zbMATH Keywords: problem reduction
reviewed by: Bernd Hofmann
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02104808
OpenAlex ID: W1976762393
description: scientific article; zbMATH DE number 917060