53 citations · 214 across the 16 of their papers we have counts for
16 papers
Restoring the Discontinuous Heat Equation Source Using Sparse Boundary Data and Dynamic Sensors
Guang Lin, Na Ou, Zecheng Zhang +1
This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired fro…
Solving the inverse potential problem in the parabolic equation by the deep neural networks method
Mengmeng Zhang, Zhidong Zhang
In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final ti…
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…
Identification of potential in diffusion equations from terminal observation: analysis and discrete approximation
Zhengqi Zhang, Zhidong Zhang, Zhi Zhou
The aim of this paper is to study the recovery of a spatially dependent potential in a (sub)diffusion equation from overposed final time data. We construct a monotone operator one…
Uniqueness and numerical inversion in the time-domain fluorescence diffuse optical tomography
Chunlong Sun, Zhidong Zhang
This work considers the time-domain fluorescence diffuse optical tomography (FDOT). We recover the distribution of fluorophores in biological tissue by the boundary measurements. W…
Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements
Guang Lin, Zecheng Zhang, Zhidong Zhang
We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from…
Recovery of the time-dependent source term in the stochastic fractional diffusion equation with heterogeneous medium
Shubin Fu, Zhidong Zhang
In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of sin…
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…
Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation
Chan Liu, Jin Wen, Zhidong Zhang
In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation…
On the identification of source term in the heat equation from sparse data
William Rundell, Zhidong Zhang
We consider the recovery of a source term for the nonhomogeneous heat equation in where is a bounded domain in with smooth…
Inverse problems for heat equation and space-time fractional diffusion equation with one measurement
Tapio Helin, Matti Lassas, Lauri Ylinen +1
Given a connected compact Riemannian manifold without boundary, , we consider a space--time fractional diffusion equation with an interior source that is suppo…
An inverse random source problem in a stochastic fractional diffusion equation
Pingping Niu, Tapio Helin, Zhidong Zhang
In this work the authors consider an inverse source problem in the following stochastic fractional diffusion equation $$\partial_t^αu(x,t)+\mathcal{A} u(x,t)=f(x)h(t)+g(x) \dot{\ma…
Recovering an Unknown Source in a Fractional Diffusion Problem
William Rundell, Zhidong Zhang
A standard inverse problem is to determine a source which is supported in an unknown domain from external boundary measurements. Here we consider the case of a time-dependent s…
An undetermined time-dependent coefficient in a fractional diffusion equation
Zhidong Zhang
In this work, we consider a FDE (fractional diffusion equation) with a time-dependent diffusion coefficient . For the direc…
Reconstruction of the Temporal Component in the Source Term of a (Time-Fractional) Diffusion Equation
Yikan Liu, Zhidong Zhang
In this article, we consider the reconstruction of in the (time-fractional) diffusion equation () by the observation at a…
Fraction diffusion: Recovering the distributed fractional derivative from overposed data
William Rundell, Zhidong Zhang
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. Th…