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We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin…

Analysis of PDEs · Mathematics 2020-10-05 Yves Capdeboscq , Roland Griesmaier , Marvin Knöller

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

We present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half-space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we…

Mathematical Physics · Physics 2020-09-07 Song Ha Nguyen , Serge Richard , Rafael Tiedra de Aldecoa

This paper is concerned with the uniqueness in inverse acoustic scattering problems with the modulus of the far-field patterns co-produced by the obstacle (resp. medium) and the point sources. Based on the superposition of point sources as…

Analysis of PDEs · Mathematics 2020-01-08 Fenglin Sun , Deyue Zhang , Yukun Guo

We provide an exact solution of the scattering problem for the potentials of the form $v(x,y)=\chi_a(x)[v_0(x)+ v_1(x)e^{i\alpha y}]$, where $\chi_a(x):=1$ for $x\in[0,a]$, $\chi_a(x):=0$ for $x\notin[0,a]$, $v_j(x)$ are real or…

Quantum Physics · Physics 2018-01-03 Farhang Loran , Ali Mostafazadeh

In this paper, we study the scattering theory for the cubic inhomogeneous Schr\"odinger equations with inverse square potential $iu_t+\Delta u-\frac{a}{|x|^2}u=\lambda |x|^{-b}|u|^2u$ with $a>-\frac14$ and $0<b<1$ in dimension three. In the…

Analysis of PDEs · Mathematics 2021-07-27 Ying Wang

We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold $M = (0,\infty) \times Y$ whose rotation radius is constant outside some compact interval. The Laplacian on $M$ is unitarily equivalent to a…

Spectral Theory · Mathematics 2019-04-19 Hiroshi Isozaki , Evgeny Korotyaev

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz…

Computational Physics · Physics 2017-10-11 Evert Klaseboer , Shahrokh Sepehrirahnama , Derek Y. C. Chan

This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz-Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive…

Numerical Analysis · Mathematics 2025-06-03 Xiaoli Liu , Shixu Meng , Jialu Tian , Bo Zhang

In this paper a wave is generated by an initial data whose support is localized at the outside of unknown obstacles and observed in a limited time on a known closed surface or the same position as the support of the initial data. The…

Analysis of PDEs · Mathematics 2020-01-27 Masaru Ikehata

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm

In this paper, we establish two sharp quantitative results for the direct and inverse time-harmonic acoustic wave scattering. The first one is concerned with the recovery of the support of an inhomogeneous medium, independent of its…

Analysis of PDEs · Mathematics 2022-01-07 Emilia L. K. Blåsten , Hongyu Liu

We consider inverse problems in space-time $(M, g)$, a $4$-dimensional Lorentzian manifold. For semilinear wave equations $\square_g u + H(x, u) = f$, where $\square_g$ denotes the usual Laplace-Beltrami operator, we prove that the…

Analysis of PDEs · Mathematics 2016-06-21 Matti Lassas , Gunther Uhlmann , Yiran Wang

An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an…

Analysis of PDEs · Mathematics 2019-02-22 Masaru Ikehata

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

Analysis of PDEs · Mathematics 2017-09-07 Peijun Li , Xiaokai Yuan

In this paper, we give a positive answer to a challenging open problem for recovering unknown obstacle (which is usually referred to as a scatterer) by acoustic wave probe associated to the Helmholtz equation. We show that the acoustic…

Analysis of PDEs · Mathematics 2021-04-20 Genqian Liu

We consider the wave equation $(\p_t^2-\Delta_g)u(t,x)=f(t,x)$, in $\R^n$, $u|_{\R_-\times \R^n}=0$, where the metric $g=(g_{jk}(x))_{j,k=1}^n$ is known outside an open and bounded set $M\subset \R^n$ with smooth boundary $\p M$. We define…

Analysis of PDEs · Mathematics 2010-11-12 Tapio Helin , Matti Lassas , Lauri Oksanen

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…

Analysis of PDEs · Mathematics 2021-07-21 Shiqi Ma , Mikko Salo

We study quantum scattering theory off $n$ point inhomogeneities ($n\in\bbN$) in three dimensions. The inhomogeneities (or generalized point interactions) positioned at $\{\xi_1,...,\xi_n\}\subset\bbR^3$ are modeled in terms of the $n^2$…

Spectral Theory · Mathematics 2007-05-23 F. Gesztesy , A. G. Ramm

An inverse obstacle scattering problem for the wave governed by the Maxwell system in the time domain, in particular, over a finite time interval is considered. It is assumed that the electric field $\mbox{\boldmath $E$}$ and magnetic field…

Analysis of PDEs · Mathematics 2018-06-25 Masaru Ikehata