arXiv subjects
Publications and source records attributed to Mourad Bellassoued.
In this paper we examine the inverse problem of determining the twisting function for the dynamicSchrodinger operator in a quantum waveguide from some suitable localized, either interior or boundary.
In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential or the magnetic field in a Schrödinger equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the magnetic Schrödinger equation. We prove that the knowledge of the Dirichlet-to-Neumann map for the Schrödinger equation uniquely determines the magnetic field and the electric potential and we establish Hölder-type stability.
In this paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schrödinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary. Namely, if the potential is known in a neighborhood of the boundary of the spatial domain, we prove that it can be logarithmic stably determined in the whole waveguide from a single observation of the solution on any arbitrary strip-shaped subset of the boundary.
We consider the nonstationary linearized Navier-Stokes equations in a bounded domain and first we prove a Carleman estimate with a regular weight function. Second we apply the Carleman estimate to a lateral Cauchy problem for the Navier-Stokes equations and prove the Hölder stability in determining the velocity and pressure field in an interior domain.
In this paper, we consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity. We establish a local Carleman estimate for Biot consilidation system. Using this estimate, we prove the uniqueness and a Hölder stability in determining on the one hand a physical parameter arising in connection with secondary consolidation effects $λ^*$ and on the other hand the two spatially varying density by a single measurement of solution over $ω\times (0, T)$, where $T>0$ is a sufficiently large time and a suitable subbdomain $ω$ satisfying $\p ω\supset \p Ω$.
We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based on an elliptic Carleman inequality.
According to Biot's paper in 1956, by using the Lagrangian equations in classical mechanics, we consider a problem of the filtration of a liquid in porous elastic-deformation media whose mechanical behavior is described by the Lam'e system coupled with a hyperbolic equation. Assuming the null surface displacement on the whole boundary, we discuss an inverse source problem of determining a body force only by observation of surface traction on a suitable subdomain along a sufficiently large time interval. Our main result is a Hölder stability estimate for the inverse source problem, which is proved by a new Carleman estimat for Biot's system.
The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a collection of quoted option prices with different strikes.
We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a Hölder stability estimate for the inverse problem, where the measurements are exerted only in some boundary components. For it, we prove a global Carleman estimate for the heterogeneous Maxwell's system with boundary conditions.
In this paper we are interested in establishing stability estimates in the inverse problem of determining on a compact Riemannian manifold the electric potential or the conformal factor in a Schrödinger equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension n bigger than 2 that the knowledge of the Dirichlet-to-Neumann map for the Schrödinger equation uniquely determines the electric potential and we establish Hölder-type stability estimates in determining the potential. We prove similar results for the determination of a conformal factor close to 1.
In this article we seek stability estimates in the inverse problem of determining the potential or the velocity in a wave equation in an anisotropic medium from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\geq 2$ that the knowledge of the Dirichlet-to-Neumann map for the wave equation uniquely determines the electric potential and we prove Hölder-type stability in determining the potential.