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This article deals with an inverse problem of identifying the fractional order in the 1D time fractional diffusion equation (TFDE in short) using the measurement at one space-time point. Based on the expression of the solution to the…

Analysis of PDEs · Mathematics 2021-11-29 Yi Zhang , Xianzheng Jia , Gongsheng Li

In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…

Analysis of PDEs · Mathematics 2026-03-11 Kuang Huang , Bangti Jin , Yavar Kian , Faouzi Triki

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

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

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…

Analysis of PDEs · Mathematics 2020-01-08 Yavar Kian , Masahiro Yamamoto

This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination…

Analysis of PDEs · Mathematics 2023-09-01 Sergey Pyatkov , Lyubov Neustroeva

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

Numerical Analysis · Mathematics 2025-01-22 Carlos Castro , Sorin Micu

We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems (including characterization): in terms of zeros of reflection coefficient and in terms of poles of reflection…

Mathematical Physics · Physics 2020-09-16 Evgeny Korotyaev , Dmitrii Mokeev

We consider a general setting for dynamic tensor field tomography in an inhomogeneous refracting and absorbing medium as inverse source problem for the associated transport equation. Following Fermat's principle the Riemannian metric in the…

Analysis of PDEs · Mathematics 2021-11-11 Lukas Vierus , Thomas Schuster

We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.

Analysis of PDEs · Mathematics 2020-01-24 Rohit Kumar Mishra , Manmohan Vashisth

In this work, the Dirac-type integro di{\S}erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal…

Spectral Theory · Mathematics 2022-03-25 Baki Keskin

Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field…

High Energy Physics - Theory · Physics 2016-03-24 Johannes Oertel , Ralf Schützhold

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

This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical result on…

Numerical Analysis · Mathematics 2021-03-26 Yikan Liu

Through coupled physics, we study an early-warning inverse source problem for the elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and…

Analysis of PDEs · Mathematics 2023-04-07 Lorenzo Baldassari , Maarten V. de Hoop , Elisa Francini , Sergio Vessella

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…

Analysis of PDEs · Mathematics 2010-02-16 Masaru Ikehata

In this paper, a time domain enclosure method for an inverse obstacle scattering problem of electromagnetic wave is introduced. The wave as a solution of Maxwell's equations is generated by an applied volumetric current having an {\it…

Analysis of PDEs · Mathematics 2016-07-22 Masaru Ikehata

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…

Numerical Analysis · Mathematics 2023-07-06 Yan Chang , Yukun Guo , Tao Yin , Yue Zhao

The method of images to solve certain electrostatic boundary-value problems is taught worldwide in undergraduate-level physics courses. Though it is also possible to employ this technique for solving magnetostatic boundary value problems,…

Classical Physics · Physics 2025-09-22 Hemansh Alkesh Shah , Kolahal Bhattacharya

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…

Numerical Analysis · Mathematics 2025-02-25 Yun Zhang , Xiaoli Feng , Xiongbin Yan