Jump to ContentJump to Main Navigation
Show Summary Details

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712

Mathematical Citation Quotient (MCQ) 2015: 0.43

249,00 € / $374.00 / £187.00*

Online
ISSN
1569-3945
See all formats and pricing
Select Volume and Issue

Issues

30,00 € / $42.00 / £23.00

Get Access to Full Text

Time-optimal reconstruction of Riemannian manifold via boundary electromagnetic measurements

1Saint-Petersburg Department of the Steklov Mathematical Institute, Russian Academy of Sciences, 191023 Saint-Petersburg, Russia.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 19, Issue 2, Pages 167–188, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2011.028, May 2011

Publication History

Received:
2011-01-30
Published Online:
2011-05-31

Abstract

A dynamical Maxwell system is et = curl h, ht = – curl e in Ω × (0, T), e|t=0 = 0, h|t=0 = 0 in Ω, eθ = ƒ in Ω × [0, T], where Ω is a smooth compact oriented 3-dimensional Riemannian manifold with boundary, (·)θ is a tangent component of a vector at the boundary, e = e ƒ (x, t) and h = h ƒ (x, t) are the electric and magnetic components of the solution. One associates with this system a response operator RT : ƒ ↦ νh ƒ|Ω×(0,T), where ν is an outward normal to Ω.

The time-optimal setup of the inverse problem, which is relevant to the finiteness of the wave speed propagation, is as follows: given R 2T to recover the part ΩT ≔ {x ∈ Ω| dist(x, ∂Ω) < T} of the manifold. As was shown by Belishev, Isakov, Pestov, Sharafutdinov (Doklady Mathematics 61: 353–356, 2000), for T small enough the operator R 2T determines ΩT uniquely up to isometry.

Here we prove that uniqueness holds for arbitrary T > 0 and provide a procedure that recovers ΩT from R 2T. Our approach is a version of the boundary control method (Belishev, 1986).

Keywords.: Maxwell system on manifold; inverse problem; reconstruction of manifold via dynamical response operator; BC-method

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
M.I. Belishev and M.N. Demchenko
Journal of Geometry and Physics, 2014, Volume 78, Page 29
[2]
M. I. Belishev and V. G. Fomenko
Journal of Mathematical Sciences, 2013, Volume 191, Number 2, Page 162
[3]
M. I. Belishev
Journal of Mathematical Sciences, 2012, Volume 185, Number 4, Page 526

Comments (0)

Please log in or register to comment.