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We prove the uniqueness in determining a spatially varying zeroth-order coefficient of a one-dimensional time-fractional diffusion equation by initial value and Cauchy data at one end point of the spatial interval.

Analysis of PDEs · Mathematics 2024-09-04 Oleg Imanuvilov , Kazufumi Ito , Masahiro Yamamoto

We consider initial boundary value problems of time-fractional advection-diffusion equations with the zero Dirichlet boundary value $\partial_t^{\alpha} u(x,t) = -Au(x,t)$, where $-A = \sum}{i,j=1}^d \partial_i(a_{ij}(x)\partial_j) +…

Analysis of PDEs · Mathematics 2021-03-30 Masahiro Yamamoto

In this work, we consider an inverse problem of determining a time dependent coefficient in a fully fractional diffusion equation with a nonlinear source term. The nonlocal initial-boundary value problem refers to the forward model: the…

Analysis of PDEs · Mathematics 2025-12-10 D. K. Durdiev , H. H. Turdiev

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

We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the smoothing properties of its solutions, which are shown to be…

Analysis of PDEs · Mathematics 2020-01-08 Xiangcheng Zheng , Jin Cheng , Hong Wang

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time variables and the zero Dirichlet boundary condition is…

Analysis of PDEs · Mathematics 2018-06-12 Adam Kubica , Masahiro Yamamoto

We consider initial boundary value problems with the homogeneous Neumann boundary condition. Given an initial value, we establish the uniqueness in determining a spatially varying coefficient of zeroth-order term by a single measurement of…

Analysis of PDEs · Mathematics 2023-05-09 Oleg Y. Imanuvilov , M. 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

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

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

An initial-boundary value problem for a subdiffusion equation with an elliptic operator $A(D)$ in $\mathbb{R}^N$ is considered. The existence and uniqueness theorems for a solution of this problem are proved by the Fourier method.…

Analysis of PDEs · Mathematics 2020-09-25 A. R. Ashurov , R. T. Zunnunov

In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique…

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

We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the…

Analysis of PDEs · Mathematics 2022-11-16 Yi-Hsuan Lin , Jesse Railo , Philipp Zimmermann

In this paper, we discuss initial-boundary value problems for linear diffusion equation with multiple time-fractional derivatives. By means of the Mittag-Leffler function and the eigenfunction expansion, we reduce the problem to an integral…

Analysis of PDEs · Mathematics 2013-11-12 Zhiyuan Li , Masahiro Yamamoto

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…

Analysis of PDEs · Mathematics 2024-10-23 Xiaohua Jing , Zhiyuan Li , Masahiro Yamamoto

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

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

In this paper, we discuss the uniqueness for solution to time-fractional diffusion equation $\partial_t^\alpha (u-u_0) + Au=0$ with the homogeneous Dirichlet boundary condition, where an elliptic operator $-A$ is not necessarily symmetric.…

Analysis of PDEs · Mathematics 2021-03-03 Daijun Jiang , Zhiyuan Li , Matthieu Pauron , Masahiro Yamamoto

In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…

Analysis of PDEs · Mathematics 2012-05-08 Yuri Luchko

In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.

Analysis of PDEs · Mathematics 2019-11-14 Suman Kumar Sahoo , Manmohan Vashisth
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