A Carleman estimate for the linear shallow shell equation and an inverse source problem

Shumin Li; Masahiro Yamamoto; Bernadette Miara

doi:10.3934/dcds.2009.23.367

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2009, Volume 23, Issue 1&2: 367-380. Doi: 10.3934/dcds.2009.23.367

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A Carleman estimate for the linear shallow shell equation and an inverse source problem

1.
Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914
2.
Laboratoire de Modélisation et Simulation Numérique, École Supérieure d'Ingenieurs en Électrotechnique et Électronique, Cité Descartes, 2 Boulevard Blaise Pascal, 93160 Noisy-le-Grand Cedex

Received: November 30, 2007

Revised: February 29, 2008

Published: April 2009

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Abstract

We consider an elastic bi-dimensional body whose reference configuration is a shallow shell. We establish a Carleman estimate for the linear shallow shell equations and apply it to prove a conditional stability for an inverse problem of determining external source terms by observations of displacement in a neighbourhood of the boundary over a time interval.

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Mathematics Subject Classification: Primary: 34A55, ; Secondary: 34A30.

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