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We show that the far--field pattern of a scattered electromagnetic field corresponding to a single incoming plane--wave uniquely determines a bounded supraconductive planar screen. This generalises a previous scalar result of Bl\aa sten,…

Analysis of PDEs · Mathematics 2023-07-20 Sadia Sadique , Petri Ola , Lassi Päivärint

We study multiple scattering off nuclei in the closure approximation. Instead of reducing the dynamics to one particle potential scattering, the scattering amplitude for fixed target configurations is averaged over the target groundstate…

Nuclear Theory · Physics 2015-06-26 S. Lenz , D. Stoll

The Born approximation of a potential in the context of the Calder\'on inverse problem is an object that can be formally defined in terms of spectral data of the Dirichlet-to-Neumann map of the corresponding Schr\"odinger operator. In this…

Analysis of PDEs · Mathematics 2026-01-21 Fabricio Macià , Cristóbal Meroño , Daniel Sánchez-Mendoza

For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincar\'e-type estimate and an energy estimate with a single observation…

Analysis of PDEs · Mathematics 2007-06-12 Patricia Gaitan

We consider elliptic transmission problems with complex coefficients across an interface. Under proper transmission conditions, that extend known conditions for well-posedness, and sub-ellipticity we derive microlocal and local Carleman…

Analysis of PDEs · Mathematics 2016-05-10 Mourad Bellassoued , Jérôme Le Rousseau

In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the…

Optimization and Control · Mathematics 2015-05-30 Qi Lu

This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…

Analysis of PDEs · Mathematics 2020-10-28 Tilo Arens , Xia Ji , Xiaodong Liu

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

We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrodinger equation for some…

Mathematical Physics · Physics 2014-11-18 Petarpa Boonserm , Matt Visser

We prove that the averaged scattering solutions to the Schr\"odinger equation with short-range electromagnetic potentials $(V,A)$ where $V(x)=O(|x|^{-\rho}), A(x)= O(|x|^{-\rho}), |x| \to \infty, \rho >1,$ are dense in the set of all…

Mathematical Physics · Physics 2020-05-22 Ricardo Weder

We consider the linear system of viscoelasticity with the homogeneous Dirichlet boundary condition. First we prove a Carleman estimate with boundary values of solutions of viscoelasticity system. Since a solution $u$ under consideration is…

Analysis of PDEs · Mathematics 2017-11-28 Oleg Imanuvilov , Masahiro Yamamoto

This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…

Analysis of PDEs · Mathematics 2017-09-26 Xiaoxu Xu , Bo Zhang , Haiwen Zhang

Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(-\beta,\beta,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely.

Mathematical Physics · Physics 2010-07-20 A. G. Ramm

The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in…

Quantum Physics · Physics 2015-05-20 Altug Arda , Oktay Aydogdu , Ramazan Sever

We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional…

Analysis of PDEs · Mathematics 2020-09-10 Manabu Machida , Masahiro Yamamoto

A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very…

Numerical Analysis · Mathematics 2017-09-13 Xiaodong Liu

A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata

This paper is concerned with the inverse elastic scattering problem to determine the shape and location of an elastic cavity. By establishing a one-to-one correspondence between the Herglotz wave function and its kernel, we introduce the…

Numerical Analysis · Mathematics 2024-09-17 Shuxin Li , Junliang Lv , Yi Wang

The problem of consistent definition of the quantum corrected gravitational field is considered in the framework of the $S$-matrix method. Gauge dependence of the one-particle-reducible part of the two-scalar-particle scattering amplitude,…

High Energy Physics - Theory · Physics 2008-11-26 Kirill A. Kazakov

We prove uniqueness and stability for the inverse boundary value problem of the two dimensional Schr\"odinger equation. We do not assume the potentials to be continuous or even bounded. Instead, we assume that some of their positive…

Analysis of PDEs · Mathematics 2017-10-04 Eemeli Blåsten