Recovery of the sound speed and initial displacement for the wave equation by means of a single Dirichlet boundary measurement

Shitao Liu

doi:10.3934/eect.2013.2.355

Article Contents

2013, Volume 2, Issue 2: 355-364. Doi: 10.3934/eect.2013.2.355

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Recovery of the sound speed and initial displacement for the wave equation by means of a single Dirichlet boundary measurement

Shitao Liu^1,

1.
Department of Mathematics and Statistics, University of Helsinki, FI-00014 Helsinki

Received: September 30, 2012

Revised: January 31, 2013

Published: May 2013

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Abstract

We consider an inverse problem of recovering simultaneously the sound speed and an initial condition for the wave equation from a single Dirichlet data measured on the boundary of the support of the initial condition. The problem is motived from the recently developed hybrid imaging models as well as from classical inverse hyperbolic problems with a single boundary measurement formulation. We establish uniqueness of the recovery and the proof is based on the Carleman estimate and continuous observability inequality for general Riemannian wave equations.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35L15.

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