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Marwa Ouni ; Abderrahmane Habbal ; Moez Kallel - A Nash-game approach to joint data completion and location of small inclusions in Stokes flow
arima:6761 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, June 29, 2021, Volume 34 - Special Issue CARI 2020 - 2021 - https://doi.org/10.46298/arima.6761A Nash-game approach to joint data completion and location of small inclusions in Stokes flowArticle
Authors: Marwa Ouni 1,2; Abderrahmane Habbal 
3,4; Moez Kallel 5
- 1 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LJAD]
- 2 Laboratoire Jean Alexandre Dieudonné
- 3 Laboratoire Jean Alexandre Dieudonné [LJAD]
- 4 Analysis and Control of Unsteady Models for Engineering Sciences
- 5 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
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.
Source: HAL:hal-02927009v3
Volume: Volume 34 - Special Issue CARI 2020 - 2021
Published on: June 29, 2021
Accepted on: June 6, 2021
Submitted on: September 7, 2020
Keywords: Data completion,Geometric inverse problem,Topological sensitivity,Calculus of variations,Nash games,Complétion des données,Jeux de Nash,Sensibilité topologique,Calculs des variations,Calcul des variations,Problème inverse géométrique,[MATH]Mathematics [math]
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