On the reconstruction of a Riemannian manifold from boundary data: The theory and plan of a numerical experiment

被引：2

作者：

Belishev M.I. ^{[1
]}

机构：

[1] St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg

来源：

Journal of Mathematical Sciences | 2011年 / 175卷 / 6期

关键词：

Russia; Manifold; Dynamical System; Numerical Experiment; Inverse Problem;

D O I：

10.1007/s10958-011-0378-7

中图分类号：

学科分类号：

摘要：

The paper deals with the inverse problem of reconstructing a Riemannian manifold from its boundary data. This problem has been solved by the boundary control method, and at the moment there are several variants of solving it. In the paper, one more version of the procedure, which recovers the manifold from scalar spectral or dynamical data, is proposed. This version is the simplest one in regard to the devices in use: geometrical optics, polar representation of operators, etc. are not employed and only a controllability property of a relevant dynamical system is applied. Without substantial changes, this version is applicable to a more complicated (vector) problem of electrodynamics for the Maxwell system. The simplicity of the procedure proposed provides additional chances for its numerical realizability. At the end of the paper, a plan of numerical experiment is discussed. To draw attention to such new options is one of the main aims of the paper. Bibliography: 9 titles. © 2011 Springer Science+Business Media, Inc.

引用

页码：623 / 636

页数：13

共 9 条

[1]

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[2]

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[3]

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[4]

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[5]

Belishev M.I., On relations between data of dynamical and spectral inverse problems, Zap. Nauchn. Semin. POMI, 297, pp. 30-48, (2003)

[6]

Belishev M.I., Recent progress in the boundary control method, Inverse Problems, 23, 5, (2007)

[7]

Belishev M.I., Demhenko M.N., Time optimal reconstruction of a Riemannian manifold via boundary electromagnetic measurements, Inverse Problems, 26, (2010)

[8]

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[9]

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