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January & February  2009, 23(1&2): 367-380. doi: 10.3934/dcds.2009.23.367

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

Shumin Li 1, , Masahiro Yamamoto 1, and  Bernadette Miara 2,

1. 

Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914, Japan, Japan
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, France

Received  December 2007 Revised  March 2008 Published  September 2008

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.
Keywords: inverse source problem, conditional stability, Carleman estimate, shallow shell.
Mathematics Subject Classification: Primary: 34A55, ; Secondary: 34A30.
Citation: Shumin Li, Masahiro Yamamoto, Bernadette Miara. A Carleman estimate for the linear shallow shell equation and an inverse source problem. Discrete & Continuous Dynamical Systems, 2009, 23 (1&2) : 367-380. doi: 10.3934/dcds.2009.23.367
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