Partial Differential Equations/Optimal Control
Detecting a moving obstacle in an ideal fluid by a boundary measurement
Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 839-844.

In this Note we investigate the problem of the detection of a moving obstacle in a perfect fluid occupying a bounded domain in R2 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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.06.007
Conca, Carlos 1; Cumsille, Patricio 1, 2; Ortega, Jaime 1, 2; Rosier, Lionel 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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Conca, Carlos; Cumsille, Patricio; Ortega, Jaime; Rosier, Lionel. 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. http://www.numdam.org/articles/10.1016/j.crma.2008.06.007/

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