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In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…

Analysis of PDEs · Mathematics 2024-12-12 Kuang Huang , Bangti Jin , Yavar Kian , Georges Sadaka , Zhi Zhou

In this paper we study the inverse problem of identifying a source or an initial state in a time-fractional diffusion equation from the knowledge of a single boundary measurement. We derive logarithmic stability estimates for both…

Analysis of PDEs · Mathematics 2021-12-22 Yavar Kian , Eric Soccorsi , Faouzi Triki

This paper is concerned with the inverse problem of determining the time and space dependent source term of diffusion equations with constant-order time-fractional derivative in $(0,2)$. We examine two different cases. In the first one, the…

Analysis of PDEs · Mathematics 2021-06-28 Yavar Kian , Eric Soccorsi , Qi Xue , Masahiro Yamamoto

This paper is concerned with an inverse problem of recovering a potential term and fractional order in a one-dimensional subdiffusion problem, which involves a Djrbashian-Caputo fractional derivative of order $\alpha\in(0,1)$ in time, from…

Analysis of PDEs · Mathematics 2021-09-22 Bangti Jin , Zhi Zhou

Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…

Numerical Analysis · Mathematics 2026-05-12 T. Catoe , V. J. Ervin

In this work, we investigate the recovery of a parameter in a diffusion process given by the order of derivation in time for a class of diffusion type equations, including both classical and time-fractional diffusion equations, from the…

Analysis of PDEs · Mathematics 2021-11-04 Bangti Jin , Yavar Kian

In this paper, we deal with the inverse source problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution does not depend continuously on the…

Probability · Mathematics 2016-11-29 Tuan Nguyen Huy , Erkan Nane

In this paper, we investigate the well-posedness and the long-time asymptotic behavior for the initial-boundary value problem for multi-term time-fractional diffusion equations, where the time differentiation consists of a finite summation…

Analysis of PDEs · Mathematics 2023-01-02 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…

Analysis of PDEs · Mathematics 2023-11-03 Xiaoli Feng , Qiang Yao , Peijun Li , Xu Wang

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

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 work, we consider a FDE (fractional diffusion equation) $${}^C D_t^\alpha u(x,t)-a(t)\mathcal{L} u(x,t)=F(x,t)$$ with a time-dependent diffusion coefficient $a(t)$. For the direct problem, given an $a(t),$ we establish the…

Analysis of PDEs · Mathematics 2019-04-08 Zhidong Zhang

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

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 paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary…

Analysis of PDEs · Mathematics 2020-04-16 Isaac Harris

This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…

Analysis of PDEs · Mathematics 2026-03-13 Mohamed BenSalah , Yikan Liu

In this paper, we study the inverse problem of finding a time-dependent multiplier of the right-hand side of a time-fractional one-dimensional diffusion equation with variables coefficients in the case where the usual Cauchy, homogeneous…

Analysis of PDEs · Mathematics 2024-11-15 D. K. Durdiev

In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…

Analysis of PDEs · Mathematics 2023-06-28 Matti Lassas , Zhiyuan Li , Zhidong Zhang

In this paper, we study an inverse problem for identifying the initial value in a space-time fractional diffusion equation from the final time data. We show the identifiability of this inverse problem by proving the existence of its unique…

Analysis of PDEs · Mathematics 2024-12-10 Mohamed BenSalah , Salih Tatar

We study the inverse backscattering problem for time-dependent potentials. We prove uniqueness and Lipshitz stability for the recovery of small potentials.

Analysis of PDEs · Mathematics 2024-07-03 Medet Nursultanov , Lauri Oksanen , Plamen Stefanov