Authors: Marwa Ouni ^1,2; Abderrahmane Habbal ^2,3; Moez Kallel ¹

• 1 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
• 2 Laboratoire Jean Alexandre Dieudonné
• 3 Analysis and Control of Unsteady Models for Engineering Sciences

We consider the coupled inverse problem of data completion and the determination of the best locations of an unknown number of small objects immersed in a stationary viscous fluid. We carefully introduce a novel method to solve this problem based on a game theory approach. A new algorithm is provided to recovering the missing data and the number of these objects and their approximate location simultaneously. The detection problem is formulated as a topological one. We present two test-cases that illustrate the efficiency of our original strategy to deal with the ill-posed problem.