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In the present work, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable…

Analysis of PDEs · Mathematics 2016-04-01 Erkinjon Karimov , Nasser Al-Salti , Sebti Kerbal

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

In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…

Analysis of PDEs · Mathematics 2018-12-24 Yu Zhao , Guanghui Hu , Baoqiang Yan

This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effective sampling schemes for location acquisition of the sources…

Analysis of PDEs · Mathematics 2018-01-18 Deyue Zhang , Yukun Guo , Jingzhi Li , Hongyu Liu

In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…

Analysis of PDEs · Mathematics 2022-11-09 Hanin Al Jebawy , Abdellatif El Badia , Faouzi Triki

A low frequency approximation of the discrete Sommerfeld diffraction problems, involving the scattering of a time harmonic lattice wave incident on square lattice by a discrete Dirichlet or a discrete Neumann half-plane, is investigated. It…

Analysis of PDEs · Mathematics 2019-08-08 Basant Lal Sharma

We prove a new uniqueness theorem for an inverse scattering problem without the phase information for the 3-D Helmholtz equation. The spatially distributed dielectric constant is the subject of the interest in this problem. We consider the…

Mathematical Physics · Physics 2017-01-03 Michael V. Klibanov

We consider an inverse source problem for the Helmholtz equation in a bounded domain. The problem is to reconstruct the shape of the support of a source term from the Cauchy data on the boundary of the solution of the governing equation. We…

Analysis of PDEs · Mathematics 2017-05-09 Masaru Ikehata

We study the inverse backscattering problem for time-dependent potentials. We prove uniqueness and Lipshitz stability for the recovery of small potentials.

Analysis of PDEs · Mathematics 2024-07-03 Medet Nursultanov , Lauri Oksanen , Plamen Stefanov

We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we…

Mathematical Physics · Physics 2015-02-17 Roman Novikov

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

Several strategies are available for solving the inverse source problem in electromagnetics. Among them, many have been focusing in retrieving Love currents by solving, after regularization, for Love's electric and magnetic currents. In…

Numerical Analysis · Mathematics 2023-05-19 Paolo Ricci , Adrien Merlini , Francesco P. Andriulli

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

We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we…

Analysis of PDEs · Mathematics 2022-08-23 Venkateswaran P. Krishnan , Rakesh , Soumen Senapati

Consider the discrete 1D Schr\"odinger operator on $\Z$ with an odd $2k$ periodic potential $q$. For small potentials we show that the mapping: $q\to $ heights of vertical slits on the quasi-momentum domain (similar to the…

Spectral Theory · Mathematics 2015-06-26 Evgeny Korotyaev , Anton Kutsenko

This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…

Numerical Analysis · Mathematics 2025-07-22 Minghui Li , Guanghui Hu , Yue Zhao

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…

Analysis of PDEs · Mathematics 2020-01-08 Yavar Kian , Masahiro Yamamoto

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…

Numerical Analysis · Mathematics 2020-02-25 Trung Truong , Dinh-Liem Nguyen , Michael Klibanov

We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…

Analysis of PDEs · Mathematics 2025-09-05 Kuang Huang , Zhiyuan Li , Zhidong Zhang , Zhi Zhou

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