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Abdessatar Khelifi

Publications and source records attributed to Abdessatar Khelifi.

6 recordsLinked to original sources
arXiv2020

Unique determination of electromagnetic parameters from partial boundary measurements

We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $Γ$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with measurements limited to an open part of the boundary and we seek to reconstruct the complex refractive index $\emph{\textbf{n}}$ in the interior of a bounded domain Further, using the impedance map restricted to $Γ$, we may identify locations of small volume fraction perturbations of the refractive index.

math-ph↗
arXiv2016

Asymptotic behaviors for eigenvalues and eigenfunctions associated to Stokes operator in the presence of small boundary perturbations

We consider the Stokes eigenvalue problem in a bounded domain of R3 with Dirich- let boundary conditions. The aim of this paper is to advance the development of high-order terms in the asymptotic expansions of the boundary perturbations of eigen- values, eigenfunctions and eigenpressures for the Stokes operator caused by small per- turbations of the boundary. Our derivation is rigorous and proved by layer potential techniques.

math-ph↗
arXiv2016

Determination of small linear perturbations in the diffusion coefficient from partial dynamic boundary measurements

This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary) dynamic boundary measurements and for finite interval in time. By constructing of appropriate test functions, using a control method, we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the diffusion coefficient as the leading order of an appropriate averaging of the partial dynamic boundary measurements.

math.AP↗
arXiv2008

Identifying of the refractive index for the acoustic equation at fixed frequency

In this paper we determine a formula for calculating the refractive index ${\bf n}$ for the acoustic equation from the partial Dirichlet to Neumann map(DN) associated to ${\bf n}$. We apply these results to identify locations and values of small volume perturbations of this refractive index at fixed frequency $ω$.

math-ph↗
arXiv2007

On the perturbation of the electromagnetic energy due to the presence of inhomogeneities with small diameters

We consider solutions to the time-harmonic Maxwell problem in $\R^3$. For such solution we provide a rigorous derivation of the asymptotic expansions in the practically interesting situation, where a finite number of inhomogeneities of small diameter are imbedded in the entire space. Then, we describe the behavior of the electromagnetic energy caused by the presence of these inhomogeneities.

math-ph↗