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In this work the authors consider an inverse source problem in the following stochastic fractional diffusion equation $$\partial_t^\alpha u(x,t)+\mathcal{A} u(x,t)=f(x)h(t)+g(x) \dot{\mathbb{W}}(t).$$ The interested inverse problem is to…

Analysis of PDEs · Mathematics 2018-10-09 Pingping Niu , Tapio Helin , Zhidong Zhang

This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…

Numerical Analysis · Mathematics 2024-01-08 Yan Chang , Yukun Guo , Yue Zhao

This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…

Numerical Analysis · Mathematics 2024-01-17 Hongxia Guo , Guanghui Hu , Guanqiu Ma

This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…

Numerical Analysis · Mathematics 2025-10-24 Kai Yu , Zhiyuan Li , Yikan Liu

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 paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the $L^2$-Tikhonov regularization method, we analyze its convergence under two…

Numerical Analysis · Mathematics 2026-01-01 Qiling Gu , Wenlong Zhang , Zhidong Zhang

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 problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse…

Analysis of PDEs · Mathematics 2018-01-11 Xianchao Wang , Minghui Song , Yukun Guo , Hongjie Li , Hongyu Liu

This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…

Numerical Analysis · Mathematics 2024-04-02 Mengjie Zhao , Suliang Si , Guanghui Hu

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

Numerical Analysis · Mathematics 2025-01-31 Zhiyuan Li , Chunlong Sun , Xiangcheng Zheng

The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…

Analysis of PDEs · Mathematics 2014-01-03 Sebastian Acosta , Sum Chow , James Taylor , Vianey Villamizar

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 inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…

Analysis of PDEs · Mathematics 2021-01-22 Guanghui Hu , Yavar Kian , Yue Zhao

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…

This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…

Analysis of PDEs · Mathematics 2018-08-01 Deyue Zhang , Yukun Guo , Jingzhi Li , Hongyu Liu

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

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

Numerical Analysis · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…

Numerical Analysis · Mathematics 2025-07-11 Yunqing Huang , Shihan Zhang

In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…

Analysis of PDEs · Mathematics 2025-03-25 Durdiev Durdimurod Kalandarovich

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
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