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In this article, for an advection-diffusion equation we study an inverse problem for restoration of source temperature from the information of final temperature profile. The uniqueness of this inverse problem is established by taking an…

Analysis of PDEs · Mathematics 2018-06-15 Zhiyuan Li , Gongsheng Li , Xianzheng Jia

This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order $\alpha\in(0,2]$ in time. In the first problem, the sources are supposed to move along known…

Analysis of PDEs · Mathematics 2023-01-03 Yikan Liu , Guanghui Hu , Masahiro Yamamoto

We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is a similar to the inverse back-scattering…

Analysis of PDEs · Mathematics 2014-03-10 Rakesh , Gunther Uhlmann

Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…

Astrophysics · Physics 2007-05-23 Norman Gray , Iain J. Coleman

Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…

Analysis of PDEs · Mathematics 2024-01-04 Sergey Grigorievich Pyatkov

We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…

Numerical Analysis · Mathematics 2022-01-24 Ylva Ljungberg Rydin , Martin Almquist

This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…

Numerical Analysis · Mathematics 2025-07-22 Minghui Li , Guanghui Hu , Yue Zhao

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…

Numerical Analysis · Mathematics 2025-04-29 Chunlong Sun , Wenlong Zhang , Zhidong Zhang

This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…

Analysis of PDEs · Mathematics 2025-01-22 Targyn A. Nauryz , Khumoyun Jabbarkhanov

In this article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interior observation. Restricting the source terms to the form of…

Analysis of PDEs · Mathematics 2021-05-26 Yavar Kian , Yikan Liu , Masahiro Yamamoto

In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1.…

Analysis of PDEs · Mathematics 2019-04-15 Yikan Liu , Zhiyuan Li , Masahiro Yamamoto

This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover…

Analysis of PDEs · Mathematics 2021-12-24 Yan Chang , Yukun Guo

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

Identification of abnormal source hidden in distributed parameter systems (DPSs) belongs to the category of inverse source problems. It is important in industrial applications but seldom studied. In this paper, we make the first attempt to…

Systems and Control · Electrical Eng. & Systems 2019-12-03 Yun Feng , Han-Xiong Li

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

Methodology · Statistics 2023-02-09 Xiao Liu , Kyongmin Yeo

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

In this article, we consider the inverse problems of determining the damping coefficient appearing in the wave equation. We prove the unique determination of the coefficient from the data coming from a single coincident source-receiver…

Analysis of PDEs · Mathematics 2019-06-24 Manmohan Vashisth

We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If…

Functional Analysis · Mathematics 2020-11-10 Tommi Brander , Joonas Ilmavirta , Petteri Piiroinen , Teemu Tyni

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Masahiro Yamamoto

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