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We consider a problem of identification of point sources in time dependent advection-diffusion systems with a non-linear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of non-linear…

Mathematical Physics · Physics 2013-09-18 Alexander V. Mamonov , Yen-Hsi Richard Tsai

We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…

Analysis of PDEs · Mathematics 2016-12-26 Yavar Kian , Diomba Sambou , Eric Soccorsi

In this paper, we investigate direct and inverse source problems for the diffusion equation with two-term generalized fractional derivative (Hilfer derivative) in a rectangular domain. Using spectral expansion method, we derive two-term…

Analysis of PDEs · Mathematics 2019-04-05 M. S. Salakhitdinov , E. T. Karimov

We study the inverse problem of determining a time-dependent globally hyperbolic Lorentzian metric from the scattering operator for semilinear wave equations.

Analysis of PDEs · Mathematics 2024-11-15 Peter Hintz , Antônio Sá Barreto , Gunther Uhlmann , Yang Zhang

Iron loss determination in the magnetic core of an electrical machine, such as a motor or a transformer, is formulated as an inverse heat source problem. The sensor positions inside the object are optimized in order to minimize the…

Numerical Analysis · Mathematics 2020-10-27 Antti Hannukainen , Nuutti Hyvönen , Lauri Perkkiö

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 study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…

Analysis of PDEs · Mathematics 2017-07-18 Gregory Eskin

For an initial-boundary value problem for a parabolic equation in the spatial variable $x=(x_1,.., x_n)$ and time $t$, we consider an inverse problem of determining a coefficient which is independent of one spatial component $x_n$ by extra…

Analysis of PDEs · Mathematics 2020-09-22 Oleg Yu. Imanuvilov , Yavar Kian , Masahiro Yamamoto

We study the existence of global-in-time solutions for a nonlinear heat equation with nonlocal diffusion, power nonlinearity and suitably small data (either compared pointwisely to the singular solution or in the norm of a critical Morrey…

Analysis of PDEs · Mathematics 2018-07-11 Piotr Biler , Dominika Pilarczyk

This paper is concerned with the uniqueness on two inverse moving source problems in electrodynamics with partial boundary data. We show that (1) if the temporal source function is compactly supported, then the spatial source profile…

Analysis of PDEs · Mathematics 2019-07-24 Guanghui Hu , Yavar Kian , Peijun Li , Yue Zhao

This paper explores the forward and inverse problems for a fractional subdiffusion equation characterized by time-dependent diffusion and reaction coefficients. Initially, the forward problem is examined, and its unique solvability is…

Analysis of PDEs · Mathematics 2025-11-10 Ravshan Ashurov , Elbek Husanov

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the…

Analysis of PDEs · Mathematics 2014-01-15 Abeer Aldoghaither , Taous-Meriem Laleg-Kirati , Da-Yan Liu

We address the inverse problem of identifying a time-dependent potential coefficient in a one-dimensional diffusion equation subject to Dirichlet boundary conditions and a nonlocal integral overdetermination constraint reflecting spatially…

Numerical Analysis · Mathematics 2025-11-12 Arshyn Altybay , Michael Ruzhansky

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 examine various density results related to the solutions of the non-local heat equation at a specific time slice, focusing on two distinct models: one with homogeneous Dirichlet boundary condition and the other with singular boundary…

Analysis of PDEs · Mathematics 2025-12-30 Saumyajit Das

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

This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…

Analysis of PDEs · Mathematics 2020-02-21 Peijun Li , Xu Wang

This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…

Numerical Analysis · Mathematics 2023-10-18 Guang Lin , Na Ou , Zecheng Zhang , Zhidong Zhang

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

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