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In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background…

Numerical Analysis · Mathematics 2023-11-23 Zhiyuan Li , Chunlong Sun

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

Numerical Analysis · Mathematics 2024-05-14 Chunlong Sun , Mengmeng Zhang , Zhidong Zhang

This paper proposes a direct inversion scheme for fluorescence diffuse optical tomography (FDOT) to reconstruct the location of a point target using the measured peak time of the temporal response functions. A sphere is defined for the…

Analysis of PDEs · Mathematics 2025-02-04 Shuli Chen , Junyong Eom , Gen Nakamura , Goro Nishimura

We investigate a hybrid inverse problem in fluorescence ultrasound modulated optical tomography (fUMOT) in the diffusive regime. We prove that the absorption coefficient of the fluorophores at the excitation frequency and the quantum…

Analysis of PDEs · Mathematics 2018-04-05 Wei Li , Yang Yang , Yimin Zhong

We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…

Analysis of PDEs · Mathematics 2026-02-27 Jiho Hong , Bangti Jin , Yavar Kian

This paper concerns an inverse problem for fluorescence diffuse optical tomography (FDOT) reconstructing locations of multiple point targets from the measured temporal response functions. The targets are multiple fluorescent point objects…

Numerical Analysis · Mathematics 2024-11-26 Shuli Chen , Junyong Eom , Gen Nakamura , Goro Nishimura

In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…

Numerical Analysis · Mathematics 2021-11-17 Bangti Jin , Yavar Kian

In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…

Analysis of PDEs · Mathematics 2020-12-02 Zhiyuan Li , Zhidong Zhang

This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Masahiro Yamamoto

In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…

Numerical Analysis · Mathematics 2025-08-19 Yikan Liu

We consider an inverse transport problem in fluorescence ultrasound modulated optical tomography (fUMOT) with angularly averaged illuminations and measurements. We study the uniqueness and stability of the reconstruction of the absorption…

Mathematical Physics · Physics 2020-02-19 Wei Li , Yang Yang , Yimin Zhong

Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…

Analysis of PDEs · Mathematics 2026-04-29 Jaan Janno

This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…

Analysis of PDEs · Mathematics 2018-08-13 Zhiyuan Li , Kenichi Fujishiro , Gongsheng Li

We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , O. Y. Imanuvilov , Masahiro Yamamoto

Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…

Analysis of PDEs · Mathematics 2019-04-12 Daijun Jiang , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…

Numerical Analysis · Mathematics 2026-04-28 Guanqiu Ma , Hongxia Guo , Guanghui Hu

This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…

Analysis of PDEs · Mathematics 2026-04-14 Jialei Li , Xiaodong Liu

In this paper, we consider the inverse problem of recovering a diffusion and absorption coefficients in steady-state optical tomography problem from the Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz stability…

Analysis of PDEs · Mathematics 2020-12-21 Houcine Meftahi

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
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