We analyze the inverse problem of the identification of a rigid body immersed in a fluid governed by the stationary Boussinesq system. First, we establish a uniqueness result. Then, we present a new method for the partial identification of the body. The proofs use local Carleman estimates, differentiation with respect to domains, data assimilation techniques and controllability results for PDEs.
On analyse le problème inverse de l'identification d'un corps rigide dans un fluide régi par le système stationnaire de Boussinesq. On établit d'abord un résultat d'unicité. Ensuite on présente une nouvelle méthode pour l'identification partielle du corps. Les preuves utilisent des estimations locales de Carleman, la différentiation par rapport au domaine, des techniques d'assimilation de données et des résultats de contrôlabilité des EDPs.
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Anna Doubova 1; Enrique Fernández-Cara 1; Manuel González-Burgos 1; Jaime Ortega 2, 3
@article{CRMATH_2006__342_9_665_0, author = {Anna Doubova and Enrique Fern\'andez-Cara and Manuel Gonz\'alez-Burgos and Jaime Ortega}, title = {Uniqueness and partial identification in a geometric inverse problem for the {Boussinesq} system}, journal = {Comptes Rendus. Math\'ematique}, pages = {665--670}, publisher = {Elsevier}, volume = {342}, number = {9}, year = {2006}, doi = {10.1016/j.crma.2006.03.006}, language = {en}, }
TY - JOUR AU - Anna Doubova AU - Enrique Fernández-Cara AU - Manuel González-Burgos AU - Jaime Ortega TI - Uniqueness and partial identification in a geometric inverse problem for the Boussinesq system JO - Comptes Rendus. Mathématique PY - 2006 SP - 665 EP - 670 VL - 342 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2006.03.006 LA - en ID - CRMATH_2006__342_9_665_0 ER -
%0 Journal Article %A Anna Doubova %A Enrique Fernández-Cara %A Manuel González-Burgos %A Jaime Ortega %T Uniqueness and partial identification in a geometric inverse problem for the Boussinesq system %J Comptes Rendus. Mathématique %D 2006 %P 665-670 %V 342 %N 9 %I Elsevier %R 10.1016/j.crma.2006.03.006 %G en %F CRMATH_2006__342_9_665_0
Anna Doubova; Enrique Fernández-Cara; Manuel González-Burgos; Jaime Ortega. Uniqueness and partial identification in a geometric inverse problem for the Boussinesq system. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 665-670. doi : 10.1016/j.crma.2006.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.006/
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