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In this article, We investigate an inverse problem of determining the time-dependent source factor in parabolic integro-differential equations from boundary data. We establish the uniqueness and the conditional stability estimate of…

Analysis of PDEs · Mathematics 2017-10-11 Atsushi Kawamoto

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

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

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

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

In this article, we provide a modified argument for proving the conditional stability of inverse source problem for a hyperbolic equation. Our method does not require any extension of solution with respect to time and therefore simplifies…

Analysis of PDEs · Mathematics 2025-06-17 Suliang Si

We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…

Analysis of PDEs · Mathematics 2025-07-15 Simone Creo , Maria Rosaria Lancia , Andrea Mola , Gianluca Mola , Silvia Romanelli

We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov, the associated cost functional is…

Analysis of PDEs · Mathematics 2022-03-22 E. M. Ait Ben Hassi , S. E. Chorfi , L. Maniar

This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…

Analysis of PDEs · Mathematics 2024-08-01 Adel Blouza , Léo Glangetas , Yavar Kian , Van-Sang Ngo

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…

Numerical Analysis · Mathematics 2022-11-23 Guang Lin , Zecheng Zhang , Zhidong Zhang

This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon…

Mathematical Physics · Physics 2013-06-21 Nazim B. Kerimov , Mansur I. Ismailov

In this article we study inverse problems of recovering a space-time dependent source component from the lateral boundary observation in a subidffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of…

Numerical Analysis · Mathematics 2021-05-19 Bangti Jin , Yavar Kian , Zhi Zhou

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

In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…

Analysis of PDEs · Mathematics 2024-10-02 Ru-Yu Lai , Hanming Zhou

In this work we investigate the inverse problem of recovering one point source in the heat equation from sparse boundary measurement, i.e., the flux data at several points on the boundary. We prove the unique recovery of the location and…

Analysis of PDEs · Mathematics 2026-03-11 Fangyu Gong , Bangti Jin , Yavar Kian , Sizhe Liu

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

In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the…

Optimization and Control · Mathematics 2015-05-30 Qi Lu

We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a…

Classical Analysis and ODEs · Mathematics 2016-04-26 Khaled M. Furati , Olaniyi S. Iyiola , Kassem Mustapha

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

We study partial data inverse problems for linear and nonlinear parabolic equations with unknown time-dependent coefficients. In particular, we prove uniqueness results for partial data inverse problems for semilinear reaction-diffusion…

Analysis of PDEs · Mathematics 2024-06-04 Ali Feizmohammadi , Yavar Kian , Gunther Uhlmann