An inverse problem for a general annular drum with positive smooth functions in the Robin boundary conditions.
An inverse problem for a general doubly-connected bounded domain with impedance boundary conditions.
An inverse problem for a nonlinear Schrödinger equation.
An inverse problem for a second-order differential equation in a Banach space.
An inverse problem for evolution inclusions.
An inverse problem for Helmholtz's equation.
An inverse problem for the equation
Let be a bounded, convex planar domain whose boundary has a not too degenerate curvature. In this paper we provide partial answers to an identification question associated with the boundary value problemWe prove two results: 1) If is not a ball and if one considers only solutions with , then there exist at most finitely many pairs of coefficients so that the normal derivative equals a given .2) If one imposes no sign condition on the solutions but one additionally supposes that is sufficiently...
An inverse problem for time-harmonic electromagnetic currents in a smoothly layered medium.
An inverse problem in a parabolic equation.
An inverse problem of the wave equation.
An inversion of the obstacle problem and its explicit solution
Anisotropic inverse problems and Carleman estimates
This note reports on recent results on the anisotropic Calderón problem obtained in a joint work with Carlos E. Kenig, Mikko Salo and Gunther Uhlmann [8]. The approach is based on the construction of complex geometrical optics solutions to the Schrödinger equation involving phases introduced in the work [12] of Kenig, Sjöstrand and Uhlmann in the isotropic setting. We characterize those manifolds where the construction is possible, and give applications to uniqueness for the corresponding anisotropic...
Application des sentinelles à l'identification des pollutions dans une rivière
Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition
We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when and the integral kernel in the nonlocal boundary condition is symmetric.
Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
We consider solutions to the time-harmonic Maxwell's Equations of a TE (transverse electric) nature. For such solutions we provide a rigorous derivation of the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter. We expect that these formulas will form the basis for very effective computational identification algorithms, aimed at determining information about the inhomogeneities from electromagnetic boundary measurements. ...
Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.
Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
In this paper, we establish Carleman estimates for the two dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and the stability in determining spatially varying density and two Lamé coefficients by a single measurement of solution over , where is a sufficiently large time interval and a subdomain satisfies a non-trapping condition.
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
In this paper, we establish Carleman estimates for the two dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and the stability in determining spatially varying density and two Lamé coefficients by a single measurement of solution over (0,T) x ω, where T > 0 is a sufficiently large time interval and a subdomain ω satisfies a non-trapping condition.