Mourad Choulli

Conditional stability in determining a heat source

We establish the uniqueness and conditional stability in determining a heat source term from boundary measurements which are started after some time. The key is analyticity of solutions in the time and we apply the maximum principle for analytic functions.

GENERIC WELL-POSEDNESS OF AN INVERSE PARABOLIC PROBLEM-THE HOLDER-SPACE APPROACH

We study an inverse parabolic problem with final overdetermination. First, we show that the solution to the direct problem depends analytically on the diffusion parameter. Then, using this fact and appropriate uniform bounds, we are able to prove generic local well-posedness of the inverse problem.

Reconstruction of the coefficients of the stationary transport equation from boundary measurements

We study the inverse problem of recovering the absorption coefficient and the collision kernel in the stationary linear Boltzmann equation in a bounded domain from the albedo operator on the boundary. We show that under some conditions on the coefficients that guarantee well-posedness of the direct problem, the inverse problem has a unique solution. Moreover, we provide explicit formulae for recovering , k.

An inverse parabolic problem with non-zero initial condition

We study the inverse problem of recovering the coefficient q(x), appearing in an initial-boundary value problem for the equation , from overdetermined final data. We prove, under some conditions, that this inverse problem is locally well-posed in around 0 when q is assumed to be a priori supported in some suitable subset.

An inverse problem for a semilinear parabolic equation

We consider the determination of a function p from overspecified data, where the function p appears in an initial-boundary value problem for the equation delta 1u- Delta u-pu+f(u)=0. The main idea in our approach consists of transforming this inverse problem into the problem of finding a solution to a non-standard non-linear equation. Using the classical Holder a priori estimates and the Schauder fixed-point theorem, we find a solution to this equation. This result then enables us to show the existence of a solution to the inverse problem. The continuous dependence of the solution to the inverse problem on the non-linear term, the boundary-value, and the overdetermined data, is also proved. Results for the linear case have already been published by the author.

An inverse problem in corrosion detection: stability estimates

In this note we correct the proof of [2, Theorem 2.1].

STABLE DETERMINATION OF A SEMILINEAR TERM IN A PARABOLIC EQUATION

In (5) the flrst and third authors establish Holder type stability estimates for the inverse problem consisting in the determination of a semilinear term of a parabolic equation from a single boundary measurement when the domain is a rectangle. In the present paper we extend the results in (5) for a general smooth domain.

Stable Determination of Time-Dependent Scalar Potential from Boundary Measurements in a Periodic Quantum Waveguide

We prove logarithmic stability in the determination of the time-dependent scalar potential in a

STABLE DETERMINATION OF A BOUNDARY COEFFICIENT IN AN ELLIPTIC EQUATION

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Stability of the determination of the surface impedance of an obstacle from the scattering amplitude

-periodic quantum cylindrical waveguide, from the boundary measurements of the solution to the dynamic Schrodinger equation.