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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 paper, we investigate the inverse problem of determining the right-hand side of a subdiffusion equation with a Caputo time derivative, where the right-hand side depends on both time and certain spatial variables. Similar inverse…

Analysis of PDEs · Mathematics 2025-05-08 R. R. Ashurov , O. T. Mukhiddinova

This paper is devoted to the study of the inverse problem of determining the right-hand side of the subdiffusion equation with the Caputo derivative with respect to time. In our case, the inverse problem consists in restoring the…

Analysis of PDEs · Mathematics 2025-05-20 R. R. Ashurov , O. T. Mukhiddinova

In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…

Analysis of PDEs · Mathematics 2022-07-15 Jaan Janno , Yavar Kian

In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian--Caputo fractional…

Numerical Analysis · Mathematics 2023-11-07 Bangti Jin , Kwancheol Shin , Zhi Zhou

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

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

This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…

Numerical Analysis · Mathematics 2025-10-24 Kai Yu , Zhiyuan Li , Yikan Liu

In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse…

Numerical Analysis · Mathematics 2020-09-09 Bangti Jin , Zhi Zhou

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 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

The work is devoted to the study of the inverse problem of determining the right-hand side of a nonlinear subdiffusion equation with a Caputo derivative with respect to time. Nonlinearity of the equation means that the right-hand side of…

Analysis of PDEs · Mathematics 2025-06-16 R. R. Ashurov , O. T. Mukhiddinova

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

We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…

Numerical Analysis · Mathematics 2024-07-23 Siyu Cen , Kwancheol Shin , Zhi Zhou

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

In the present paper we consider an inverse source problem for time-fractional mixed parabolic-hyperbolic equation with the Caputo derivative. In case, when hyperbolic part of the considered mixed type equation is wave equation, the…

Analysis of PDEs · Mathematics 2015-12-08 Pengbin Feng , E. T. Karimov

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

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

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…

Numerical Analysis · Mathematics 2026-05-08 Siyu Cen , Bangti Jin , Yavar Kian , Zhi Zhou

The subdiffusion model that involves a Caputo fractional derivative in time is widely used to describe anomalously slow diffusion processes. In this work we aim at recovering the locations of small conductivity inclusions in the model from…

Numerical Analysis · Mathematics 2025-05-29 Jiho Hong , Bangti Jin , Zhizhang Wu

In this paper, we focus on a space-time fractional diffusion equation with the generalized Caputo's fractional derivative operator and a general space nonlocal operator (with the fractional Laplace operator as a special case). A weak…

Analysis of PDEs · Mathematics 2016-06-07 Junxiong Jia , Jigen Peng , Jiaqing Yang
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