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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 839-844 (août 2008)
Doi : 10.1016/j.crma.2008.06.007
Received : 7 January 2008 ;  accepted : 18 June 2008
Detecting a moving obstacle in an ideal fluid by a boundary measurement
Détection dʼun obstacle en mouvement dans un fluide parfait à partir dʼune mesure sur le bord du domaine

Carlos Conca a , Patricio Cumsille a, b , Jaime Ortega a, b , Lionel Rosier a, c
a 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 
b Depto. Ciencias Básicas, Fac. Ciencias, U. del Bío-Bío, Avda Andrés Bello, Chillán, Chile 
c Institut Élie-Cartan, UMR 7502 UHP/CNRS/INRIA, B.P. 239, 54506 Vandœuvre-lès-Nancy cedex, France 


In this Note we investigate the problem of the detection of a moving obstacle in a perfect fluid occupying a bounded domain in   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. To cite this article: C. Conca et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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Dans cette Note, on sʼintéresse au problème de la détection dʼun 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 lʼobstacle est une boule, on montre que la position et la vitesse de son centre de gravité peuvent être identifiées à lʼaide dʼune seule mesure. La stabilité linéaire par rapport à la mesure est prouvée par des techniques de différentiation par rapport au domaine. Pour citer cet article : C. Conca et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.

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