English
Related papers

Related papers: Inverse acoustic scattering problem in half-space …

200 papers

This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. We show…

Mathematical Physics · Physics 2015-05-13 Guillaume Bal , Alexandre Jollivet

We consider a polyhedron with zero classical resistance, i.e., a polyhedron invisible to an observer viewing only the paths of geometrical optics rays. The corresponding problem of scattering of plane waves by the polyhedron is studied. The…

Mathematical Physics · Physics 2012-04-19 E. Lakshtanov , B. D. Sleeman , B. Vainberg

The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…

Numerical Analysis · Mathematics 2023-02-15 Carlos Borges , Manas Rachh , Leslie Greengard

This paper investigates an inverse random source problem for the stochastic fractional Helmholtz equation. The source is modeled as a centered, complex-valued, microlocally isotropic generalized Gaussian random field whose covariance and…

Analysis of PDEs · Mathematics 2026-02-24 Peijun Li , Zhenqian Li

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

This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…

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

Inverse scattering focuses on recovering unknown scatterers from wave measurements. A fundamental challenge is determining whether an inverse obstacle problem can be resolved from a single far-field measurement, a task particularly…

Analysis of PDEs · Mathematics 2026-04-15 Huaian Diao , Hongyu Liu , Longyue Tao

This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…

Analysis of PDEs · Mathematics 2019-12-02 Xueshuang Xiang , Hongpeng Sun

We investigate the numerical implementation of the limiting equation for the phonon transport equation in the small Knudsen number regime. The main contribution is that we derive the limiting equation that achieves the second order…

Numerical Analysis · Mathematics 2025-10-13 Anjali Nair , Qin Li , Weiran Sun

Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects…

Signal Processing · Electrical Eng. & Systems 2020-12-17 Ajinkya Kadu , Hassan Mansour , Petros T. Boufounos

In this paper we study the behavior of the solutions to the Robin problem in bounded $1$-sided NTA domains with Ahlfors-David regular boundary, generalizing the results of \cite{DavDEMM} to the case of a non constant Robin parameter. In…

Analysis of PDEs · Mathematics 2025-10-28 Svitlana Mayboroda , Alberto Pacati

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Numerical Analysis · Mathematics 2020-02-03 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky , Jörn Zimmerling

This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally…

Analysis of PDEs · Mathematics 2021-12-28 Jianliang Li , Peijun Li , Xu Wang

We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of…

Spectral Theory · Mathematics 2011-09-30 Alexei Iantchenko , Evgeny Korotyaev

In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…

Statistics Theory · Mathematics 2023-11-30 Aksel Kaastrup Rasmussen , Fanny Seizilles , Mark Girolami , Ieva Kazlauskaite

In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…

Analysis of PDEs · Mathematics 2022-02-24 Hongyu Liu , Chun-Hsiang Tsou

In this article, the inverse scattering problem (ISP) of recovering the matrix coefficient of a first order system of ordinary differential equations on the half-axis from its scattering matrix is considered. In the case of a triangular…

Spectral Theory · Mathematics 2013-07-02 Mansur I. Ismailov

We consider the partial data inverse boundary problem for the Schr\"odinger operator at a frequency $k>0$ on a bounded domain in $\mathbb{R}^n$, $n\ge 3$, with impedance boundary conditions. Assuming that the potential is known in a…

Analysis of PDEs · Mathematics 2019-07-23 Katya Krupchyk , Gunther Uhlmann

This article deals with the inverse problem of determining the unbounded real-valued electric potential of the Robin Laplacian on a bounded domain of dimension 3 or greater, by incomplete knowledge of its boundary spectral data. Namely, the…

Analysis of PDEs · Mathematics 2025-07-10 Mourad Choulli , Abdelmalek Metidji , Eric Soccorsi

We are concerned with the acoustic scattering problem, at a frequency $\kappa$, by many small obstacles of arbitrary shapes with impedance boundary condition. These scatterers are assumed to be included in a bounded domain $\Omega$ in…

Analysis of PDEs · Mathematics 2016-10-20 Durga Prasad Challa , Mourad Sini