Academic Journal
Nash strategies for the inverse inclusion Cauchy-Stokes problem
| العنوان: | Nash strategies for the inverse inclusion Cauchy-Stokes problem |
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| المؤلفون: | Habbal, Abderrahmane, Kallel, Moez, Ouni, Marwa |
| المساهمون: | Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA), Analysis and Control of Unsteady Models for Engineering Sciences (ACUMES), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur Tunis (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), PHC Utique Namred 2018-2020 |
| المصدر: | ISSN: 1930-8337. |
| بيانات النشر: | HAL CCSD AIMS American Institute of Mathematical Sciences |
| سنة النشر: | 2019 |
| المجموعة: | HAL Université Côte d'Azur |
| مصطلحات موضوعية: | Data completion, Cauchy-Stokes problem, shape identification, Nash games, Primary: 49J20, 65K10, Secondary: 65N06, 90C30, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] |
| الوصف: | International audience ; We introduce a new algorithm to solve the problem of detecting unknown cavities immersed in a stationary viscous fluid, using partial boundarymeasurements. The considered fluid obeys a steady Stokes regime, the cavities are inclusions and the boundary measurements are a single compatible pair of Dirichlet and Neumann data, available only on a partial accessible part of the whole boundary. This inverse inclusion Cauchy-Stokes problem is ill-posed for both the cavities and missing data reconstructions, and designing stable and efficient algorithms is not straightforward. We reformulate the problem as a three-player Nash game. Thanks to an identifiability result derived for the Cauchy-Stokes inclusion problem, it is enough to set up two Stokes boundary value problems, then use them as state equations. The Nash game is then set between 3 players, the two first targeting the data completion while the third one targets the inclusion detection. We used a level-set approach to get rid of the tricky control dependence of functional spaces, and we provided the third player with the level-set function as strategy, with a cost functional of Kohn-Vogelius type. We propose an original algorithm, which we implemented using Freefem++. We present 2D numerical experiments for three different test-cases.The obtained results corroborate the efficiency of our 3-player Nash game approach to solve parameter or shape identification for Cauchy problems. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| DOI: | 10.3934/ipi.2019038 |
| الاتاحة: | https://inria.hal.science/hal-01945094 https://inria.hal.science/hal-01945094v1/document https://inria.hal.science/hal-01945094v1/file/Habbal_Kallel_Ouni_v0.pdf https://doi.org/10.3934/ipi.2019038 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.3485B36E |
| قاعدة البيانات: | BASE |
| DOI: | 10.3934/ipi.2019038 |
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