[Détection d'un obstacle en mouvement dans un fluide parfait à partir d'une mesure sur le bord du domaine]
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.
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.
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@article{CRMATH_2008__346_15-16_839_0,
author = {Conca, Carlos and Cumsille, Patricio and Ortega, Jaime and Rosier, Lionel},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.06.007/}
}
TY - JOUR AU - Conca, Carlos AU - Cumsille, Patricio AU - Ortega, Jaime AU - Rosier, Lionel TI - Detecting a moving obstacle in an ideal fluid by a boundary measurement JO - Comptes Rendus. Mathématique PY - 2008 SP - 839 EP - 844 VL - 346 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.06.007/ DO - 10.1016/j.crma.2008.06.007 LA - en ID - CRMATH_2008__346_15-16_839_0 ER -
%0 Journal Article %A Conca, Carlos %A Cumsille, Patricio %A Ortega, Jaime %A Rosier, Lionel %T Detecting a moving obstacle in an ideal fluid by a boundary measurement %J Comptes Rendus. Mathématique %D 2008 %P 839-844 %V 346 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.06.007/ %R 10.1016/j.crma.2008.06.007 %G en %F CRMATH_2008__346_15-16_839_0
Conca, Carlos; Cumsille, Patricio; Ortega, Jaime; Rosier, Lionel. Detecting a moving obstacle in an ideal fluid by a boundary measurement. Comptes Rendus. Mathématique, Tome 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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