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Russian Mathematical Surveys, 2017, Volume 72, Issue 4, Pages 581–644
DOI: https://doi.org/10.1070/RM9768 (Mi rm9768) 		 
This article is cited in 40 scientific papers (total in 40 papers)

Boundary control and tomography of Riemannian manifolds (the BC-method)

M. I. Belishevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Russia
b St. Petersburg State University, Russia
English version PDF (1121 kB) Citations (40)
References:
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DOI: https://doi.org/10.1070/RM9768
Abstract: The BC-method provides one of the approaches to inverse problems of mathematical physics. A characteristic feature of this method is the great variety of interdisciplinary relations involved: in addition to partial differential equations as a source of problems, use is made of control theory and systems theory, asymptotic methods, functional analysis, operator theory, Banach algebras, and so on. The purpose of this paper is to present the principal ideas and tools of the BC-method and to give a survey of some results. One of the main achievements of the method is chosen for presentation: the reconstruction of Riemannian manifolds from dynamical and spectral boundary data.
Bibliography: 108 titles.
Keywords: inverse problems, reconstruction of Riemannian manifolds from boundary data, the BC-method.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00529-а
Volkswagen Foundation
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 17-01-00529-a) and the Volkswagen Foundation.
Received: 06.03.2017
Revised: 10.05.2017
Russian version:
Uspekhi Matematicheskikh Nauk, 2017, Volume 72, Issue 4(436), Pages 3–66
DOI: https://doi.org/10.4213/rm9768
Bibliographic databases:
Document Type: Article
UDC: 517.954+517.956.37+517.98
MSC: 35R30, 58J32, 35Q93, 35L10, 47L90, 46L99, 35R02
Language: English
Original paper language: Russian
Citation: M. I. Belishev, “Boundary control and tomography of Riemannian manifolds (the BC-method)”, Uspekhi Mat. Nauk, 72:4(436) (2017), 3–66; Russian Math. Surveys, 72:4 (2017), 581–644
Citation in format AMSBIB
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    • This publication is cited in the following 40 articles:
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    Russian version PDF:138
    English version PDF:31
    References:73
    First page:59
     
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