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We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

Analysis of PDEs · Mathematics 2018-08-01 Ngoc Do , Leonid Kunyansky

This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…

Analysis of PDEs · Mathematics 2026-03-13 Mohamed BenSalah , Yikan Liu

We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…

Analysis of PDEs · Mathematics 2024-10-31 Safiere Kuijpers , Laura Scarabosio

In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly…

Analysis of PDEs · Mathematics 2018-01-09 Youjun Deng , Hongyu Liu , Xiaodong Liu

This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…

Analysis of PDEs · Mathematics 2025-07-29 Yavar Kian , Hongyu Liu

In this paper, we consider the inverse source problem for the time-fractional diffusion equation, which has been known to be an ill-posed problem. To deal with the ill-posedness of the problem, we propose to transform the problem into a…

Numerical Analysis · Mathematics 2021-08-27 Bin Fan , Chuanju Xu

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…

Analysis of PDEs · Mathematics 2018-04-04 Gang Bao , Guanghui Hu , Yavar Kian , Tao Yin

We study the modulational instability of small-amplitude periodic traveling wave solutions in a dispersion generalized Ostrovsky equation. Specifically, we investigate the invertibility of the associated linearized operator in the vicinity…

Analysis of PDEs · Mathematics 2024-09-25 Bhavna , Mathew A. Johnson , Ashish Kumar Pandey

In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…

Analysis of PDEs · Mathematics 2023-11-03 Xiaoli Feng , Qiang Yao , Peijun Li , Xu Wang

In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…

Analysis of PDEs · Mathematics 2021-04-21 Isaac Harris

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…

Numerical Analysis · Mathematics 2017-08-03 Guan Wang , Fuming Ma , Yukun Guo , Jingzhi Li

The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…

Optics · Physics 2009-09-15 Albert C. Fannjiang

We investigate an inverse source problem of the time-harmonic elastic wave equation. Some novel sampling-type numerical schemes are proposed to identify the moment tensor point sources in the Lam\'e system from near-field measurements.…

Numerical Analysis · Mathematics 2021-11-24 Xianchao Wang , Yukun Guo , Sara Bousba

We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…

Analysis of PDEs · Mathematics 2020-04-29 Jingzhi Li , Hongyu Liu , Shiqi Ma

We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We…

Analysis of PDEs · Mathematics 2022-02-25 Wei Li , John C. Schotland , Yang Yang , Yimin Zhong

In this paper we consider convex Tikhonov regularisation for the solution of linear operator equations on Hilbert spaces. We show that standard fractional source conditions can be employed in order to derive convergence rates in terms of…

Optimization and Control · Mathematics 2020-02-24 Markus Grasmair

In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…

Analysis of PDEs · Mathematics 2020-12-10 Fang Zeng , Shixu Meng

This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical…

Analysis of PDEs · Mathematics 2021-06-25 Peijun Li , Xu Wang

A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…

Numerical Analysis · Mathematics 2019-04-02 Alexey V. Smirnov , Michael V. Klibanov , Loc H. Nguyen

We consider the first and half order time fractional equation with the zero initial condition. We investigate an inverse source problem of determining the time-independent source factor by the data at an arbitrarily fixed time and we…

Analysis of PDEs · Mathematics 2016-11-17 Atsushi Kawamoto