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This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…

Numerical Analysis · Mathematics 2020-08-26 Barbara Kaltenbacher , William Rundell

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

This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…

Analysis of PDEs · Mathematics 2026-04-13 Ravshan Ashurov , Damir Shamuratov

The paper considers an inverse source problem for a one-dimensional time-fractional heat equation with the generalized impedance boundary condition. The inverse problem is the time dependent source parameter identification together with the…

Analysis of PDEs · Mathematics 2016-09-06 M. Cicek , M. I. Ismailov

In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…

Numerical Analysis · Mathematics 2021-11-17 Bangti Jin , Yavar Kian

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 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

In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…

Numerical Analysis · Mathematics 2020-05-06 Daijun Jiang , Yikan Liu , Dongling Wang

In this paper, we investigate the inverse problem of determining the right-hand side of a subdiffusion equation with a Caputo time derivative, where the right-hand side depends on both time and certain spatial variables. Similar inverse…

Analysis of PDEs · Mathematics 2025-05-08 R. R. Ashurov , O. T. Mukhiddinova

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

We consider an inverse source problem in the two-time-scale mobile-immobile fractional diffusion model from partial interior observation. Theoretically, we combine the fractional Duhamel's principle with the weak vanishing property to…

Numerical Analysis · Mathematics 2026-04-02 Zhiwei Yang , Yikan Liu

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

We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…

This paper investigates an inverse random source problem for the stochastic fractional Helmholtz equation. The source is modeled as a centered, complex-valued, microlocally isotropic generalized Gaussian random field whose covariance and…

Analysis of PDEs · Mathematics 2026-02-24 Peijun Li , Zhenqian Li

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

Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements…

Analysis of PDEs · Mathematics 2025-05-06 Hany Gerges , Jaan Janno

In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique…

Analysis of PDEs · Mathematics 2023-01-02 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…

Analysis of PDEs · Mathematics 2016-09-14 Jaan Janno , Kairi Kasemets

Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…

Analysis of PDEs · Mathematics 2026-04-29 Jaan Janno

In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…

Analysis of PDEs · Mathematics 2025-07-10 D. K. Durdiev , H. H. Turdiev , A. A. Rahmonov