Detecting a moving obstacle in an ideal fluid by a boundary measurement

Carlos Conca; Patricio Cumsille; Jaime Ortega; Lionel Rosier

doi:10.1016/j.crma.2008.06.007

Partial Differential Equations/Optimal Control

Detecting a moving obstacle in an ideal fluid by a boundary measurement

Presented by: Gilles Lebeau

Carlos Conca ¹; Patricio Cumsille ^1,²; Jaime Ortega ^1,²; Lionel Rosier ^1,³

¹ Departamento de Ingeniería Matemática (DIM) and Centro de Modelamiento Matemático (CMM), Universidad de Chile (UMI CNRS 2807), Avda Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile
² Depto. Ciencias Básicas, Fac. Ciencias, U. del Bío-Bío, Avda Andrés Bello, Chillán, Chile
³ Institut Élie-Cartan, UMR 7502 UHP/CNRS/INRIA, B.P. 239, 54506 Vandœuvre-lès-Nancy cedex, France

Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 839-844.

Abstract
Résumé

In this Note we investigate the problem of the detection of a moving obstacle in a perfect fluid occupying a bounded domain in $R^{2}$ from the measurement of the velocity of the fluid on one part of the boundary. We show that when the obstacle is a ball, we may identify the position and the velocity of its center of mass from a single boundary measurement. Linear stability estimates are also established by using shape differentiation techniques.

Dans cette Note, on s'intéresse au problème de la détection d'un obstacle en mouvement dans un fluide parfait incompressible à partir de la mesure de la vitesse du fluide sur une partie du bord du domaine. Lorsque l'obstacle est une boule, on montre que la position et la vitesse de son centre de gravité peuvent être identifiées à l'aide d'une seule mesure. La stabilité linéaire par rapport à la mesure est prouvée par des techniques de différentiation par rapport au domaine.

Received: 2008-01-07
Accepted: 2008-06-18
Published online: 2008-07-25

DOI: 10.1016/j.crma.2008.06.007

Author's affiliations:

Carlos Conca ¹; Patricio Cumsille ^{1, 2}; Jaime Ortega ^{1, 2}; Lionel Rosier ^{1, 3}

¹ Departamento de Ingeniería Matemática (DIM) and Centro de Modelamiento Matemático (CMM), Universidad de Chile (UMI CNRS 2807), Avda Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile
² Depto. Ciencias Básicas, Fac. Ciencias, U. del Bío-Bío, Avda Andrés Bello, Chillán, Chile
³ Institut Élie-Cartan, UMR 7502 UHP/CNRS/INRIA, B.P. 239, 54506 Vandœuvre-lès-Nancy cedex, France

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     author = {Carlos Conca and Patricio Cumsille and Jaime Ortega and Lionel Rosier},
     title = {Detecting a moving obstacle in an ideal fluid by a boundary measurement},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {839--844},
     publisher = {Elsevier},
     volume = {346},
     number = {15-16},
     year = {2008},
     doi = {10.1016/j.crma.2008.06.007},
     language = {en},
}

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Carlos Conca; Patricio Cumsille; Jaime Ortega; Lionel Rosier. Detecting a moving obstacle in an ideal fluid by a boundary measurement. Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 839-844. doi : 10.1016/j.crma.2008.06.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.06.007/

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