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.6761
A Nash-game approach to joint data completion and location of small inclusions in Stokes flowArticle

Authors: Marwa Ouni 1,2; Abderrahmane Habbal ORCID2,3; 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.


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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