OUNI , Marwa

This thesis aims to study the ability of theoretic game approaches to deal with ill-posed problems. The first part of the thesis is dedicated to the Stokes system's linear problem, with the goal of detecting unknown geometric inclusions or pointwise sources in a stationary viscous fluid, using a single compatible pair of Dirichlet and Neumann...

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We consider linear steady Stokes flow under the action of a finite number of particles located inside the flow domain. The particles exert point-wise forces on the fluid, and are unknown in number, location and magnitude. We are interested in the determination of these point-wise forces, using only a single pair of partially available Cauchy...

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...

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...

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...

We consider linear steady Stokes flow under the action of a finite number of particles located inside the flow domain. The particles exert point-wise forces on the fluid, and are unknown in number, location and magnitude. We are interested in the determination of these point-wise forces, using only a single pair of partially available Cauchy...