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Dive into the research topics where Abdellatif El Badia is active.

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Featured researches published by Abdellatif El Badia.


Inverse Problems | 2005

Inverse source problem in an anisotropic medium by boundary measurements

Abdellatif El Badia

In this paper, we consider an inverse source problem for an anisotropic elliptic equation, from boundary measurements. A uniqueness result is established and a local Lipshitz stability, for a linear combination of monopolar and dipolar sources, is discussed. Assuming the number of dipoles bounded by a given integer M, we propose an algebraic algorithm which allows us to estimate the number, the locations and the moments of dipoles. Using special functions, we propose a global Lipschitz stability estimate for dipolar sources.


Inverse Problems | 2011

An inverse source problem for Helmholtz's equation from the Cauchy data with a single wave number

Abdellatif El Badia; Takaaki Nara

The inverse source problem of the Helmholtz equation in an interior domain is investigated. We show the uniqueness and local stability, where the source consists of multiple point sources. An algebraic algorithm is proposed to identify the number, locations and intensities of the point sources from boundary measurements. Uniqueness and non-uniqueness results for some distributed sources are also established. The proposed method is verified numerically.


Inverse Problems | 2007

Inverse source problem in an advection–dispersion–reaction system: application to water pollution

Abdellatif El Badia; Adel Hamdi

In this paper, we consider the problem of identifying an unknown source F( x, t)= λ(t)δ(x − S) in the following system: (∂t − D∂xx + V∂ x + R)u(x, t) = F( x, t), 0 <x<� , 0 <t < T (∂t − D∂xx + V∂ x + R)v(x, t) = Ru(x, t), 0 <x<� , 0 <t < T from measured data [{v(a, t), ∂xv(a, t)}, {v(b, t), ∂xv(b, t)}] for appropriate points a and b. Assuming that the source F became inactive after the time T ∗ (i.e .λ (t)= 0f ort T ∗ ), we prove an identifiability result and propose an identification method. (Some figures in this article are in colour only in the electronic version)


Inverse Problems | 2013

Inverse dipole source problem for time-harmonic Maxwell equations: algebraic algorithm and Hölder stability

Abdellatif El Badia; Takaaki Nara

In this paper, we investigate an inverse source problem of the time harmonic Maxwell equations at a fixed frequency, where the source consists of multiple point dipoles. An algebraic algorithm is proposed to identify the number, locations and moments of the dipoles from boundary measurements of tangential components of the electric and magnetic fields. Also, a H?lder stability result is shown. The proposed algorithm is numerically verified.


Inverse Problems | 2015

Direct algorithms for solving some inverse source problems in 2D elliptic equations

Batoul Abdelaziz; Abdellatif El Badia; Ahmad El Hajj

This paper deals with the resolution of some inverse source problems in the 2D elliptic equation from Cauchy data. Two types of sources are considered, pointwise sources and sources having compact support within a finite number of small subdomains. An identification direct algorithm, based on an algebraic approach, is proposed. This is a new result, as far as we know, except in the case which is already considered in El Badia and Ha-Duong (2000 Inverse Problems 16 651?63).


Inverse Problems | 2013

Stability estimates for an inverse source problem of Helmholtz’s equation from single Cauchy data at a fixed frequency

Abdellatif El Badia; Ahmad El Hajj

This paper deals with an inverse pointwise source problem for the Helmholtz equation in the three-dimensional case from single Cauchy data at a fixed frequency. Stability estimates of locations, intensities and moments for monopolar and dipolar sources are established.


Journal of Inverse and Ill-posed Problems | 2010

An inverse source problem for quasi-static Maxwell's equations

Abdellatif El Badia; Takaaki Nara

Abstract In this paper, we show the uniqueness and local stability of an inverse source problem for the quasi-static Maxwell equation in a layered domain, where the source consists of multiple point dipoles. Also, an algebraic algorithm is proposed to identify the number, locations, and moments of the dipoles from boundary measurements of tangential components of the electric and magnetic fields. The proposed algorithm is numerically verified.


Journal of Mathematical Analysis and Applications | 2015

Direct algorithm for multipolar sources reconstruction

Batoul Abdelaziz; Abdellatif El Badia; Ahmad El Hajj


Comptes Rendus Mathematique | 2013

Reconstruction of extended sources with small supports in the elliptic equation from a single Cauchy data

Batoul Abdelaziz; Abdellatif El Badia; Ahmad El Hajj


Comptes Rendus Mathematique | 2012

Hölder stability estimates for some inverse pointwise source problems

Abdellatif El Badia; Ahmad El Hajj

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Ahmad El Hajj

École des ponts ParisTech

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Takaaki Nara

University of Electro-Communications

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Abdelaziz Batoul

University of Technology of Compiègne

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Adel Hamdi

Institut national des sciences appliquées de Rouen

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