89 research outputs found
Reconstruction of interfaces from the elastic farfield measurements using CGO solutions
In this work, we are concerned with the inverse scattering by interfaces for
the linearized and isotropic elastic model at a fixed frequency. First, we
derive complex geometrical optic solutions with linear or spherical phases
having a computable dominant part and an -decaying remainder term
with , where is the classical Sobolev space. Second,
based on these properties, we estimate the convex hull as well as non convex
parts of the interface using the farfields of only one of the two reflected
body waves (pressure waves or shear waves) as measurements. The results are
given for both the impenetrable obstacles, with traction boundary conditions,
and the penetrable obstacles. In the analysis, we require the surfaces of the
obstacles to be Lipschitz regular and, for the penetrable obstacles, the Lam\'e
coefficients to be measurable and bounded with the usual jump conditions across
the interface.Comment: 32 page
Stable determination of a scattered wave from its far-field pattern: the high frequency asymptotics
We deal with the stability issue for the determination of outgoing
time-harmonic acoustic waves from their far-field patterns. We are especially
interested in keeping as explicit as possible the dependence of our stability
estimates on the wavenumber of the corresponding Helmholtz equation and in
understanding the high wavenumber, that is frequency, asymptotics.
Applications include stability results for the determination from far-field
data of solutions of direct scattering problems with sound-soft obstacles and
an instability analysis for the corresponding inverse obstacle problem.
The key tool consists of establishing precise estimates on the behavior of
Hankel functions with large argument or order.Comment: 49 page
On the one dimensional Gelfand and Borg-Levinson spectral problems for discontinuous coefficients
In this paper, we deal with the inverse spectral problem for the equation -(pu')'+qu = \lambda\rho u on a finite interval (0; h). We give some uniqueness results on q and \rho from the Gelfand spectral data, when the coefficients p and \rho are piecewise Lipschitz and q is bounded. We also prove an equivalence result between the Gelfand spectral data and the Borg-Levinson spectral data. As a consequence, we have similar uniqueness results if we consider the Borg-Levinson spectral data. Finally, we consider the inverse problem from the nodes and give uniqueness results on \rho and in the case where the coefficients p; q and \rho are smooth we give a uniqueness results on both q and \rho
- …