Global Carleman estimate on a network for the wave equation and application to an inverse problem

Lucie Baudouin; Emmanuelle Crépeau; Julie Valein

doi:10.3934/mcrf.2011.1.307

Article Contents

2011, Volume 1, Issue 3: 307-330. Doi: 10.3934/mcrf.2011.1.307

This issue Previous Article Recent results on the controllability of linear coupled parabolic problems: A survey Next Article Internal stabilization of a Mindlin-Timoshenko model by interior feedbacks

Global Carleman estimate on a network for the wave equation and application to an inverse problem

1.
CNRS; LAAS; 7 avenue du colonel Roche, F-31077 Toulouse Cedex 4
2.
Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin en Yvelines, F-78035 Versailles
3.
Institut Elie Cartan de Nancy & INRIA (Project-Team CORIDA), BP 239, F-54506 Vandœuvre-les-Nancy Cedex

Received: February 28, 2011

Revised: April 30, 2011

Published: August 2011

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Abstract

We are interested in an inverse problem for the wave equation with potential on a star-shaped network. We prove the Lipschitz stability of the inverse problem consisting in the determination of the potential on each string of the network with Neumann boundary measurements at all but one external vertices. Our main tool, proved in this article, is a global Carleman estimate for the network.

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Mathematics Subject Classification: 35R30, 93C20, 34B45.

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