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Consider an isotropic elastic medium $\Omega \subset \mathbb{R}^3$ whose Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only…

Analysis of PDEs · Mathematics 2019-03-14 Peter Caday , Maarten V. de Hoop , Vitaly Katsnelson , Gunther Uhlmann

This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…

Analysis of PDEs · Mathematics 2020-08-26 Sophia Bugarija , Peter C. Gibson , Guanghui Hu , Peijun Li , Yue Zhao

We consider an isotropic elastic medium occupying a bounded domain D whose density and Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave…

Analysis of PDEs · Mathematics 2022-03-17 Sombuddha Bhattacharyya , Maarten V. de Hoop , Vitaly Katsnelson , Gunther Uhlmann

Consider the acoustic wave equation with unknown, not necessarily smooth, wave speed $c$. We propose and study an iterative control procedure that erases the history of a wave field up to a given depth in a medium, without any knowledge of…

Analysis of PDEs · Mathematics 2018-08-29 Peter Caday , Maarten V. de Hoop , Vitaly Katsnelson , Gunther Uhlmann

In this paper, we study an inverse problem for an acoustic-gravitational system whose principal symbol is identical to that of an acoustic wave operator. The displacement vector of a gas or liquid between the unperturbed and perturbed flow…

Analysis of PDEs · Mathematics 2024-10-10 Sombuddha Bhattacharyya , Maarten de Hoop , Vitaly Katsnelson

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…

Analysis of PDEs · Mathematics 2017-11-02 Li Jingzhi , Liu Hongyu , Sun Hongpeng

This paper addresses the inverse scattering problem in the domain Omega. The input data, measured outside Omega, involve the waves generated by the interaction of plane waves with various directions and unknown scatterers fully occluded…

Numerical Analysis · Mathematics 2024-06-25 Phuong M. Nguyen , Loc H. Nguyen , Huong T. T. Vu

This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…

Numerical Analysis · Mathematics 2017-10-16 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen

The unique reconstruction of a spherically-symmetric wave speed $v$ is considered in a bounded spherical region of radius $b$ from the set of corresponding transmission eigenvalues for which the corresponding eigenfunctions are also…

Spectral Theory · Mathematics 2018-05-22 Tuncay Aktosun , Vassilis G. Papanicolaou

An inverse boundary value problem for the 1+1 dimensional wave equation $(\partial_t^2 - c(x)^2 \partial_x^2)u(x,t)=0,\quad x\in\mathbb{R}_+$ is considered. We give a discrete regularization strategy to recover wave speed $c(x)$ when we are…

Analysis of PDEs · Mathematics 2018-03-29 Jussi Korpela , Matti Lassas , Lauri Oksanen

We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…

Mathematical Physics · Physics 2015-06-12 Adrianna Gillman , Alex Barnett

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

We analyze the inverse problem, originally formulated by Dix in geophysics, of reconstructing the wave speed inside a domain from boundary measurements associated with the single scattering of seismic waves. We consider a domain $\tilde M$…

Analysis of PDEs · Mathematics 2012-12-04 Maarten V. de Hoop , Sean F. Holman , Einar Iversen , Matti Lassas , Bjørn Ursin

This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field…

Numerical Analysis · Mathematics 2024-05-09 Xiaoxu Xu , Guanqiu Ma , Guanghui Hu

We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…

Analysis of PDEs · Mathematics 2025-02-21 Zhenhao Li , Jian Wang , Jared Wunsch

The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…

Atomic Physics · Physics 2015-06-03 I. Hornyak , A. T. Kruppa

We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic…

Analysis of PDEs · Mathematics 2026-03-30 Adrian Kirkeby

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge

This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…

Analysis of PDEs · Mathematics 2018-12-26 Alexey Agaltsov , Thorsten Hohage , Roman Novikov

Scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is the wave…

Numerical Analysis · Mathematics 2016-02-16 Alexander Ramm , Nhan Tran
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