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Documents  Bellassoued, Mourad | enregistrements trouvés : 6

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Research talks;Partial Differential Equations;Mathematical Physics

I discuss several types of inverse problems for fluid dynamics such as Navier-Stokes equations. I prove uniqueness and conditional stability for the formulations by Dirichlet-to-Neumann map and Carleman estimates. This is a joint work with Prof. O. Imanuvilov (Colorado State Univ.)

35R30

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Research talks;Partial Differential Equations

This talk is devoted to the study of the following inverse boundary value problem: given a Riemannian manifold with boundary determine the magnetic potential in a dynamical Schrödinger equation in a magnetic field from the observations made at the boundary.

inverse problem - Schrödinger equation - magnetic field

35R30 ; 35Q55 ; 35R35 ; 35Q60

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Research talks;Partial Differential Equations

The anisotropic Calderon problem is whether it is possible to determine a Riemannian metric (modulo the natural invariance by isometries) on a compact Riemannian manifold with boundary from knowledge of the Cauchy data of harmonic functions. This problem is solved in dimension two, as well as in the conformal class of the Euclidean metric and for analytic metrics, but remains challenging for smooth metrics in dimension higher than three. In this talk I will present recent results in the case of a conformal class of metrics presenting a special structure of (warped) product with an Euclidean factor. I will explain how the identifiability of the conformal factor can be deduced from the injectivity of a certain geodesic ray transform in the transversal part of the manifold. In the case of independence with respect to the Euclidean variable, a direct link with the corresponding hyperbolic problem (which can be solved using the Boundary control method) can be made. This extends previous results of C. Kenig, M. Salo, G. Uhlmann and myself where stronger geometric assumptions were made.
This is a joint work with S. Kurylev (University College London), M. Lassas (University of Helsinki) and M. Salo (University of Jyvaskyla)
The anisotropic Calderon problem is whether it is possible to determine a Riemannian metric (modulo the natural invariance by isometries) on a compact Riemannian manifold with boundary from knowledge of the Cauchy data of harmonic functions. This problem is solved in dimension two, as well as in the conformal class of the Euclidean metric and for analytic metrics, but remains challenging for smooth metrics in dimension higher than three. In this ...

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Research talks;Partial Differential Equations

In this talk, I will present a method introduced in 2010 by Cristofol and Roques to obtain uniqueness results in inverse problems of determining non-constant coefficients of nonlinear parabolic equations. This method is mainly based on the Hopf's lemma and on the parabolic maximum principle. It can be applied to several types of 1D reaction-diffusion equations and systems, such as the Fisher-KPP equation and Lotka-Volterra competition systems.

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Research talks;Partial Differential Equations

Several recent coupled-physics medical imaging modalities aim to combine a high-contrast, low-resolution, modality with a high-resolution, low-contrast, modality and ideally offer high-contrast, high-resolution, reconstructions. Such modalities often involve the reconstruction of constitutive parameters in partial differential equations (PDE) from knowledge of internal functionals of the parameters and PDE solutions. This talk presents several recent results of uniqueness, stability and explicit reconstructions for several hybrid inverse problems. In particular, we provide explicit characterizations of what can (and cannot) be reconstructed and offer optimal (elliptic) stability estimates for a large class of coupled-physics imaging modalities including Magnetic Resonance Elastography, Transient Elastography, Photo-Acoustic Tomography and Ultrasound Modulation Tomography. Numerical simulations confirm the high-resolution, high-contrast, potential of these novel modalities. Several recent coupled-physics medical imaging modalities aim to combine a high-contrast, low-resolution, modality with a high-resolution, low-contrast, modality and ideally offer high-contrast, high-resolution, reconstructions. Such modalities often involve the reconstruction of constitutive parameters in partial differential equations (PDE) from knowledge of internal functionals of the parameters and PDE solutions. This talk presents several ...

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Research talks;Partial Differential Equations

In the talk I will present results of uniqueness and stability related to the reconstruction of the refractive index of a medium using multifrequency scattering data.

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