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This article is cited in 46 scientific papers (total in 46 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
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.
Received: 06.03.2017 Revised: 10.05.2017
Citation:
M. I. Belishev, “Boundary control and tomography of Riemannian manifolds (the BC-method)”, Russian Math. Surveys, 72:4 (2017), 581–644
Linking options:
https://www.mathnet.ru/eng/rm9768https://doi.org/10.1070/RM9768 https://www.mathnet.ru/eng/rm/v72/i4/p3
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Abstract page: | 732 | Russian version PDF: | 155 | English version PDF: | 48 | References: | 94 | First page: | 59 |
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