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November  2006, 6(6): 1213-1238. doi: 10.3934/dcdsb.2006.6.1213

A geometric inverse problem for the Boussinesq system

A. Doubov 1, , Enrique Fernández-Cara 2, , Manuel González-Burgos 3, and  J. H. Ortega 4,

1. 

Universidad de Sevilla, Dpto. E.D.A.N., Aptdo. 1160, 41080, Sevilla, Spain
2. 

Dpto., E.D.A.N., Universidad de Sevilla, Aptdo. 1180; 41080 Sevilla
3. 

Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla
4. 

Universidad del Bío-Bío, Dpto. de Ciencias Básicas, Casilla 447, Fernando May, Chillán, Chile

Received  November 2005 Revised  June 2006 Published  August 2006

In this work we present some results for the inverse problem of the identification of a single rigid body immersed in a fluid governed by the stationary Boussinesq equations. First, we establish a uniqueness result. Then, we show the way the observation depends on perturbations of the rigid body and we deduce some consequences. Finally, we present a new method for the partial identification of the body assuming that it can be deformed only through fields that, in some sense, are finite dimensional. In the proofs, we use various techniques, related to Carleman estimates, differentiation with respect to domains, data assimilation and controllability of PDEs.
Keywords: inverse problem, data assimilation, Boussinesq system, differentiation with respect to domains, controllability..
Mathematics Subject Classification: 35LXX, 34K2.
Citation: A. Doubov, Enrique Fernández-Cara, Manuel González-Burgos, J. H. Ortega. A geometric inverse problem for the Boussinesq system. Discrete and Continuous Dynamical Systems - B, 2006, 6 (6) : 1213-1238. doi: 10.3934/dcdsb.2006.6.1213
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