Determination of point-forces via extended boundary
measurements using a game strategy approach
Marwa OUNI* — Abderrahmane HABBAL** —Moez KALLEL*
* Université de Tunis El Manar, Ecole Nationale d’Ingénieur de Tunis,
Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur B.P. 37, 1002 Tunis, Tunisie
** Université Côte d’Azur, Inria, CNRS,
LJAD, UMR 7351, Parc Valrose 06108 NICE CEDEX 2, France
ABSTRACT. In this work, we consider a game theory approach to deal with an inverse problem related to the Stokes system. The problem consists in detecting the unknown point-forces acting on the fluid from incomplete measurements on the boundary of a domain. The approach that we propose deals simultaneously with the reconstruction of the missing data and the determination of the unknown point-forces. The solution is interpreted in terms
of Nash equilibrium between both problems. We develop a new point-force detection algorithm, and we present numerical results to illustrate the efficiency and robustness of the method.
KEYWORDS : Nash game, data completion, point-forces detection.