Zakaria Belhachmi

Learn More
We introduce and discuss shape based models for finding the best interpolation data when reconstructing missing regions in images by means of solving the Laplace equation. The shape analysis is done in the framework of Γ-convergence, from two different points of view. First, we propose a continuous PDE model and get pointwise information on the ”importance”(More)
This paper is devoted to an elementary introduction to the homogenization method applied to topology and shape optimization of elastic structures under single and multiple external loads. The single load case, in the context of minimum compliance and weight design of elastic structures, has been fully described in its theoretical as well as its numerical(More)
The paper deals with the identifiability of non-smooth defects by boundary measurements, and the stability of their detection. We introduce and analyse a new pointwise regularity concept at the boundary of an open set which turns out to play a crucial role in the identifiabilty of defects by two boundary measurements. As a consequence, we prove the unique(More)
Applying high order finite elements to unilateral contact variational inequalities may provide more accurate computed solutions, compared with linear finite elements. Up to now, there was no significant progress in the mathematical study of their performances. The main question is involved with the modeling of the nonpenetration Signorini condition on the(More)
We consider a variational model for the determination of the optic-flow in a general setting of non-smooth domains. This problem is ill-posed and its solution with PDE techniques includes a regularization procedure. The goal of this paper is to study a method to solve the optic flow problem and to control the effects of the regularization by allowing,(More)
Any solution of the Navier–Stokes equations in a three-dimensional axisymmetric domain admits a Fourier expansion with respect to the angular variable, and it can be noted that each Fourier coefficient satisfies a variational problem on the meridian domain, all problems being coupled due to the nonlinear convection term. We propose a discretization of these(More)