220 citations · 812 across the 28 of their papers we have counts for
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Simultaneous uniqueness for a coefficient inverse problem in one-dimensional fractional diffusion equation from an interior point measurement
Xiaohua Jing, 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 e…
Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems
Matti Lassas, Zhiyuan Li, Zhidong Zhang
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…
Initial-boundary value problems for coupled systems of time-fractional diffusion equations
Zhiyuan Li, Xinchi Huang, Yikan Liu
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamen…
Uniqueness and stability for inverse source problem for fractional diffusion-wave equations
Xing Cheng, Zhiyuan Li
This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at s…
Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions
Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
In this paper, we obtain the sharp uniqueness for an inverse -source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum pos…
Well-posedness and asymptotic estimate for a diffusion equation with time-fractional derivative
Zhiyuan Li, Xinchi Huang, Masahiro Yamamoto
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary c…
Strong positivity property and a related inverse source problem for multi-term time-fractional diffusion equations
Xiaona Yang, Zhiyuan Li
In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive that the solution is positive when the source term is nonpositive b…
Uniqueness for fractional nonsymmetric diffusion equations and an application to an inverse source problem
Daijun Jiang, Zhiyuan Li, Matthieu Pauron +1
In this paper, we discuss the uniqueness for solution to time-fractional diffusion equation with the homogeneous Dirichlet boundary condition, where an…
Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data
Zhiyuan Li, Zhidong Zhang
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…
Well-posedness for the backward problems in time for general time-fractional diffusion equation
Giuseppe Floridia, Zhiyuan Li, Masahiro Yamamoto
In this article, we consider a partial differential equation with Caputo time-derivative: where and satisfies the zero Dirichlet boundary con…
Unique determination of several coefficients in a fractional diffusion(-wave) equation by a single measurement
Yavar Kian, Zhiyuan Li, Yikan Liu +1
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…
Inverse Problems of Determining Coefficients of the Fractional Partial Differential Equations
Zhiyuan Li, Masahiro Yamamoto
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the…
Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations
Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractio…
Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
Yikan Liu, Zhiyuan Li, Masahiro Yamamoto
In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order . Our surve…
Unique continuation principle for the one-dimensional time-fractional diffusion equation
Zhiyuan Li, Masahiro Yamamoto
This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order . Firstly, the uniqueness o…
A novel method to solve inverse source problem for advection-diffusion equation from final data
Zhiyuan Li, Gongsheng Li, Xianzheng Jia
In this article, for an advection-diffusion equation we study an inverse problem for restoration of source temperature from the information of final temperature profile. The unique…
Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients
Zhiyuan Li, Xinchi Huang, Masahiro Yamamoto
In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffl…
Initial-boundary value problem for distributed order time-fractional diffusion equations
Zhiyuan Li, Yavar Kian, Eric Soccorsi
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak soluti…
An inverse problem for distributed order time-fractional diffusion equations
Zhiyuan Li, Kenichi Fujishiro, Gongsheng Li
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…
Carleman estimates for the time-fractional advection-diffusion equations and applications
Zhiyuan Li, Xinchi Huang, Masahiro Yamamoto
In this article, we prove Carleman estimates for the generalized time-fractional advection-diffusion equations by considering the fractional derivative as perturbation for the firs…
Conditional stability for an inverse source problem for the time-fractional diffusion equation
Zhiyuan Li
This paper deals with an inverse source problem for the D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the un…
Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations
Daijun Jiang, Zhiyuan Li, Yikan Liu +1
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…
Asymptotic behavior of solutions to space-time fractional diffusion equations
Xing Cheng, Zhiyuan Li, Masahiro Yamamoto
This article discusses the analyticity and the long-time asymptotic behavior of solutions to space-time fractional diffusion equations in . By a Laplace transform arg…
Uniqueness in inverse boundary value problems for fractional diffusion equations
Zhiyuan Li, O. Y. Imanuvilov, Masahiro Yamamoto
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-…