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Related papers: The point source inverse back-scattering problem

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The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

Problem for a cubic string having the shape of a step is studied. It is proved that here we have two scattering problems: the direct one and its dual. The direct problem describes scattering of the waves coming from ``$+\infty$'', and its…

Classical Analysis and ODEs · Mathematics 2025-09-09 Vladimir A. Zolotarev

We study the direct and inverse scattering problems when the incident electromagnetic field is a time harmonic point- generated wave in a chiral medium and the scatterer is a perfectly conducting sphere. The exact Green s function and the…

Classical Physics · Physics 2008-12-12 Nikolaos Berketis , Christodoulos Athanasiadis

In this paper, we investigate on the direct and inverse scattering problem by an unbounded penetrable rough surface in a lossless medium. The cases that the transmission coefficient $\mu\neq1$ and $\mu=1$, which creates certain difficulties…

Analysis of PDEs · Mathematics 2025-11-25 Chengyu Wu , Jiaqinq Yang

An inverse problem is considered for an inhomogeneous Schr\"odinger equation. Assuming that the potential vanishes outside a finite interval and satisfies some other technical assumptions, one proves the uniqueness of the recovery of this…

Mathematical Physics · Physics 2009-10-31 A. G. Ramm

We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…

Optics · Physics 2012-08-23 Johannes Skaar , Magnus W. Haakestad

Inverse scattering problem for the operator representing sum of the operator of the third derivative on semi-axis and of the operator of multiplication by a real function is studied in this paper. Properties of Jost solutions of such an…

Functional Analysis · Mathematics 2023-06-06 Vladimir A. Zolotarev

Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…

Analysis of PDEs · Mathematics 2012-06-27 A. G. Ramm

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants.…

Spectral Theory · Mathematics 2007-05-23 R. O. Hryniv , Ya. V. Mykytyuk

We study the inverse backscattering problem for the Schr\"odinger equation in two dimensions. We prove that, for a non-smooth potential in 2D the main singularities up to 1/2 of the derivative of the potential are contained in the Born…

Analysis of PDEs · Mathematics 2012-09-14 Juan Manuel Reyes

We consider the inverse problem of recovering the optical properties of a highly-scattering medium from acousto-optic measurements. Using such measurements, we show that the scattering and absorption coefficients of the radiative transport…

Analysis of PDEs · Mathematics 2016-09-27 Francis J Chung , John C Schotland

We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…

Mathematical Physics · Physics 2023-07-31 Tadayoshi Adachi , Yuta Tsujii

We consider the direct and inverse scattering problem for a penetrable, isotropic obstacle with a second-order Robin boundary condition, which asymptotically models the delamination of the boundary of the scatterer. We develop a direct…

Analysis of PDEs · Mathematics 2026-01-22 Govanni Granados , Isaac Harris , Andreas Kleefeld

We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, the exiting radiation is measured on an arc. The attenuation and scattering…

Analysis of PDEs · Mathematics 2021-11-17 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from…

Mathematical Physics · Physics 2009-11-11 Ricardo Weder , Dimitri Yafaev

The paper considers an inverse source problem for a one-dimensional time-fractional heat equation with the generalized impedance boundary condition. The inverse problem is the time dependent source parameter identification together with the…

Analysis of PDEs · Mathematics 2016-09-06 M. Cicek , M. I. Ismailov

We solve the inverse spectral problem for rotationally symmetric manifolds, which include the class of surfaces of revolution, by giving an analytic isomorphism from the space of spectral data onto the space of functions describing the…

Mathematical Physics · Physics 2016-05-18 Hiroshi Isozaki , Evgeny L. Korotyaev

Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…

Numerical Analysis · Mathematics 2022-10-17 Bangti Jin , Yavar Kian , Zhi Zhou

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…

The inverse scattering problem on the half-line has been studied in the literature in detail. V. Marchenko presented the solution to this problem. In this paper, the invertibility of the steps of the inversion procedure is discussed and a…

Mathematical Physics · Physics 2016-01-12 A. G. Ramm