Publication Cover
Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 3
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Original Articles

Stability estimate for an inverse problem for the wave equation in a magnetic field

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Pages 277-292 | Received 12 Oct 2007, Accepted 11 Jan 2008, Published online: 19 Mar 2008
 

Abstract

In this article, we prove stability estimate of the inverse problem of determining the magnetic field entering the magnetic wave equation in a bounded smooth domain in ℝ d from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the magnetic wave equation. We prove in dimension d ≥ 2 that the knowledge of the Dirichlet-to-Neumann map for the magnetic wave equation measured on the boundary determines uniquely the magnetic field and we prove a Hölder-type stability in determining the magnetic field induced by the magnetic potential.

Acknowledgement

The authors thank the anonymous referee for very useful comments.

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