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This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…

Analysis of PDEs · Mathematics 2026-03-03 Ravshan Ashurov , Damir Shamuratov

We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of…

Analysis of PDEs · Mathematics 2023-11-17 Piermarco Cannarsa , Anna Doubova , Masahiro Yamamoto

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 for a diffusion equation containing a generalized fractional derivative are studied. The equation holds in a time interval $(0,T)$ and it is assumed that a state $u$ (solution of diffusion equation) and a source $f$ are…

Mathematical Physics · Physics 2024-02-02 Jaan Janno

We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known…

Analysis of PDEs · Mathematics 2024-05-03 Rohit Kumar Mishra , Anamika Purohit , Manmohan Vashisth

This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary…

Numerical Analysis · Mathematics 2023-07-10 Siyu Cen , Bangti Jin , Yikan Liu , Zhi Zhou

The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…

Numerical Analysis · Mathematics 2023-08-08 Siyu Cen , Zhi Zhou

The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a…

Analysis of PDEs · Mathematics 2020-01-14 Nikolai Dokuchaev

Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…

Analysis of PDEs · Mathematics 2024-12-23 S. G. Pyatkov , O. A. Soldatov

In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the…

Analysis of PDEs · Mathematics 2024-03-19 Siyu Cen , Bangti Jin , Yavar Kian , Eric Soccorsi , Rachid Zarouf , Zhi Zhou

There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…

Analysis of PDEs · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

Inverse problem for multi-term fractional parabolic equation in two dimensional space, involving m + 1 Caputo fractional derivatives in time, is investigated. Presence of nonlocal boundary conditions leads to a non-self-adjoint spectral…

Analysis of PDEs · Mathematics 2022-02-08 Muhammad Ali , Sara Aziz

In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…

Numerical Analysis · Mathematics 2015-06-04 Bangti Jin , William Rundell

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 work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,\omega).$ We build the…

Analysis of PDEs · Mathematics 2020-04-09 Shubin Fu , Zhidong Zhang

This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…

Numerical Analysis · Mathematics 2025-02-06 Dmitrii Chaikovskii , Ye Zhang , Aleksei Liubavin

The problem of reconstructing the drift of a diffusion in $\erre^d$, $d\geq 2$, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of…

Probability · Mathematics 2007-06-13 Sergio Albeverio , Carlo Marinelli

Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…

Numerical Analysis · Mathematics 2022-10-17 Bangti Jin , Yavar Kian , Zhi Zhou

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

In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space variable but also on the time variable. More precisely, we attempt to stably and…

Analysis of PDEs · Mathematics 2018-10-05 Mourad Bellassoued , Ibtissem Ben Aïcha