A control approach to recover the wave speed (conformal factor) from one measurement

Sebastian Acosta

doi:10.3934/ipi.2015.9.301

Article Contents

2015, Volume 9, Issue 2: 301-315. Doi: 10.3934/ipi.2015.9.301

This issue Previous Article Recovery of the absorption coefficient in radiative transport from a single measurement Next Article On the range of the attenuated magnetic ray transform for connections and Higgs fields

A control approach to recover the wave speed (conformal factor) from one measurement

Sebastian Acosta^1,

1.
Department of Pediatrics - Cardiology, Baylor College of Medicine, Houston, TX

Received: December 31, 2013

Revised: December 31, 2014

Published: April 2015

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Abstract

In this paper we consider the problem of recovering the conformal factor in a conformal class of Riemannian metrics from the boundary measurement of one wave field. More precisely, using boundary control operators, we derive an explicit equation satisfied by the contrast between two conformal factors (or wave speeds). This equation is Fredholm and generically invertible provided that the domain of interest is properly illuminated at an initial time. We also show locally Lipschitz stability estimates.

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Mathematics Subject Classification: Primary: 35L05, 35R30; Secondary: 35Q93.

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