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In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…

Analysis of PDEs · Mathematics 2025-08-11 Rahmonov Askar Ahmadovich

Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…

Analysis of PDEs · Mathematics 2025-06-02 Chun Liu , Guanghui Hu , Tao Yin , Bo Zhang

We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…

Analysis of PDEs · Mathematics 2024-03-21 Tianjiao Wang , Xiang Xu , Yue Zhao

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

This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…

Analysis of PDEs · Mathematics 2025-03-14 Tianjiao Wang , Xiang Xu , Yue Zhao

This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…

Analysis of PDEs · Mathematics 2025-09-22 Xu Wang , Guanlin Yang , Zhidong Zhang

This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…

Analysis of PDEs · Mathematics 2020-04-22 Xiaoli Feng , Peijun Li , Xu Wang

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…

Mathematical Physics · Physics 2024-02-13 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

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

This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…

Numerical Analysis · Mathematics 2024-01-02 Hongxia Guo , Guanghui Hu

We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of…

Analysis of PDEs · Mathematics 2022-10-13 Peijun Li , Xu Wang

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

Analysis of PDEs · Mathematics 2018-08-17 Gang Bao , Peijun Li , Yue Zhao

This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source…

Numerical Analysis · Mathematics 2022-12-12 Hongxia Guo , Guanghui Hu , Mengjie Zhao

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

Analysis of PDEs · Mathematics 2017-09-07 Peijun Li , Xiaokai Yuan

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

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,…

Analysis of PDEs · Mathematics 2021-04-27 Ru-Yu Lai , Hanming Zhou

Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…

Analysis of PDEs · Mathematics 2018-08-08 Xia Ji , Xiaodong Liu , Bo Zhang

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

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…

Analysis of PDEs · Mathematics 2019-06-07 Xia Ji , Xiaodong Liu