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We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…

Spectral Theory · Mathematics 2025-08-18 Lung-Hui Chen

The focusing operation inherent to the linear discrete inverse problem is formalised. The development is given in the context of sound-field reproduction where the source strengths are the inverse solution needed to recreate a prescribed…

Audio and Speech Processing · Electrical Eng. & Systems 2020-11-19 Eric C. Hamdan , Filippo Maria Fazi

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…

Analysis of PDEs · Mathematics 2019-04-12 Daijun Jiang , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither…

Analysis of PDEs · Mathematics 2022-11-02 David Omogbhe , Kamran Sadiq

Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…

Analysis of PDEs · Mathematics 2023-11-29 General Ozochiawaeze

We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…

Numerical Analysis · Mathematics 2012-10-30 Adriano De Cezaro , B. Tomas Johansson

Sound scattering by a finite width beam on a single rigid body rotation vortex flow is detected by a linear array of transducers (both smaller than a flow cell), and analyzed using a revised scattering theory. Both the phase and amplitude…

Chaotic Dynamics · Physics 2009-11-10 Sh. Seifer , V. Steinberg

This work is concerned with an inverse scattering problem of determining unknown scatterers from time-dependent acoustic measurements. A novel time-domain direct sampling method is developed to efficiently determine both the locations and…

Numerical Analysis · Mathematics 2023-12-08 Yukun Guo , Hongjie Li , Xianchao Wang

We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…

Analysis of PDEs · Mathematics 2021-02-19 Zhengjian Bai , Huaian Diao , Hongyu Liu , Qingle Meng

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

Analysis of PDEs · Mathematics 2025-07-02 Jianliang Li , Peijun Li , Xu Wang , Guanlin Yang

This paper is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a random potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian…

Analysis of PDEs · Mathematics 2021-03-23 Jianliang Li , Peijun Li , Xu Wang

We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across $\Sigma\subseteq\Gamma=\partial\Omega$, where $\Omega$ is a bounded open subset of $\mathbb{R}^{3}$ with a Lipschitz…

Analysis of PDEs · Mathematics 2018-06-08 Andrea Mantile , Andrea Posilicano , Mourad Sini

Atmospheric lidar observations provide a unique capability to directly observe the vertical column of cloud and aerosol scattering properties. Detector and solar background noise, however, hinder the ability of lidar systems to provide…

Optimization and Control · Mathematics 2016-06-21 Willem J. Marais , Robert E. Holz , Yu Hen Hu , Ralph E. Kuehn , Edwin E. Eloranta , Rebecca M. Willett

This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…

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

This study addresses the inverse source problem for the fractional diffusion-wave equation, characterized by a source comprising spatial and temporal components. The investigation is primarily concerned with practical scenarios where data…

Numerical Analysis · Mathematics 2025-04-22 Lingyun Qiu , Jiwoon Sim

Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate.…

Numerical Analysis · Mathematics 2024-03-27 Matthew Nethercote , Anastasia Kisil , Raphael Assier

We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…

Analysis of PDEs · Mathematics 2021-11-24 Jianli Xiang , Guanghui Hu

A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…

Optimization and Control · Mathematics 2022-09-28 William W. Symes

We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…

Numerical Analysis · Mathematics 2026-05-13 Raaghav Ramani

The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…

Numerical Analysis · Mathematics 2026-04-29 Yukun Guo , Xiaodong Liu