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This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…

Analysis of PDEs · Mathematics 2025-04-25 Qi Lü , Yu Wang

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…

Analysis of PDEs · Mathematics 2020-01-08 Xia Ji , Xiaodong Liu

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

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

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

We propose in this paper a globally numerical method to solve a phaseless coefficient inverse problem: how to reconstruct the spatially distributed refractive index of scatterers from the intensity (modulus square) of the full complex…

Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…

Analysis of PDEs · Mathematics 2019-09-09 Shahah Almutairi , Ajith Gunaratne

This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…

Numerical Analysis · Mathematics 2025-07-29 Zhiqi Sun , Yiwen Lin

Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…

Analysis of PDEs · Mathematics 2019-06-06 Phuong Mai Nguyen , Loc Hoang Nguyen

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

In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…

Numerical Analysis · Mathematics 2023-10-16 Abinand Gopal , Jeremy Hoskins , Vladimir Rokhlin

This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…

Analysis of PDEs · Mathematics 2018-12-03 Jianliang Li , Tapio Helin , Peijun Li

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

Analysis of PDEs · Mathematics 2016-08-10 Gang Bao , Chuchu Chen , Peijun Li

This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where the source is assumed to be driven by a Gaussian random field. The direct problem is shown to be well-posed by…

Numerical Analysis · Mathematics 2020-12-22 Yuxuan Gong , Peijun Li , Xu Wang , Xiang Xu

We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering…

Numerical Analysis · Mathematics 2020-02-11 Deyue Zhang , Yukun Guo , Fenglin Sun , Xianchao Wang

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…

Optimization and Control · Mathematics 2021-03-30 Konstantin Pieper , Bao Quoc Tang , Philip Trautmann , Daniel Walter

The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR)…

Numerical Analysis · Mathematics 2016-09-14 Balgaisha Mukanova , Vladimir G. Romanov

In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…

Numerical Analysis · Mathematics 2025-08-22 Tianhao Hu , Xinchi Huang , Bangti Jin , Qimeng Quan , Zhi Zhou

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

Analysis of PDEs · Mathematics 2018-12-03 Heping Dong , Jun Lai , Peijun Li

This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…

Numerical Analysis · Mathematics 2025-06-30 Thuy T. Le , Phuong M. Nguyen , Loc H. Nguyen