EDPS paraboliques à coefficients non—lipschitziens avec réflexion
Elastic wave equation
The goal of this talk is to describe the Lamé operator which drives the propagation of linear elastic waves. The main motivation for me is the work I have done in collaboration with Michel Campillo’s group from LGIT (Grenoble) on passive imaging in seismology. From this work, several mathematical problems emerged: equipartition of energy between and waves, high frequency description of surface waves in a stratified medium and related inverse spectral problems.We discuss the following topics:What...
Electrical impedance tomography in nonlinear media
Enhanced electrical impedance tomography via the Mumford–Shah functional
We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...
Enhanced Electrical Impedance Tomography via the Mumford–Shah Functional
We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...
Équations d'évolution non linéaires : solutions bornées et périodiques
Soit un sous-différentiel (non coercif) dans un espace de Hilbert.On étudie l’existence de solutions bornées ou périodiques pour l’équationDeux solutions périodiques éventuelles diffèrent d’une constante. Si est périodique et compact, toute trajectoire bornée est asymptote pour à une trajectoire périodique.
Erratum of article “Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems”
Erratum of article “Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems”
Erratum to Fourier diffraction theorem for the tensor fields
Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method
The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.
Estimates in the Hardy-Sobolev space of the annulus and stability result
The main purpose of this work is to establish some logarithmic estimates of optimal type in the Hardy-Sobolev space ; of an annular domain. These results are considered as a continuation of a previous study in the setting of the unit disk by L. Baratchart and M. Zerner, On the recovery of functions from pointwise boundary values in a Hardy-Sobolev class of the disk, J. Comput. Appl. Math. 46 (1993), 255–269 and by S. Chaabane and I. Feki, Optimal logarithmic estimates in Hardy-Sobolev spaces...
Estimation of a temporally and spatially varying diffusion coefficinet in a parabolic system by an augmented Lagrangian technique.
Estimation of the conductivity in the one-phase Stefan problem : numerical results
Exact boundary observability for quasilinear hyperbolic systems
By means of a direct and constructive method based on the theory of semi-global C1 solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case.
Existence of a nonstationary Poiseuille solution.