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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2017 Volume 72, Issue 4(436), Pages 3–66 (Mi rm9768)

This article is cited 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.

UDC: 517.954+517.956.37+517.98

MSC: 35R30, 58J32, 35Q93, 35L10, 47L90, 46L99, 35R02

Received: 06.03.2017
Revised: 10.05.2017

DOI: 10.4213/rm9768


 English version:
Russian Mathematical Surveys, 2017, 72:4, 581–644

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© Steklov Math. Inst. of RAS, 2025