6 papers
A monotone iterative reconstruction method for an inverse drift problem in a two-dimensional parabolic equation
Liuying Zhang, Wenlong Zhang, Zhidong Zhang
We study an inverse drift problem for a two-dimensional parabolic equation on the unit square with mixed boundary conditions, where the drift coefficient is recovered from terminal…
Inverse source problem for the parabolic equation with sparse moving observations
Qiling Gu, Wenlong Zhang, Zhidong Zhang
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unk…
An efficient iteration method to reconstruct the drift term from the final measurement
Dakang Cen, Wenlong Zhang, Zhidong Zhang
This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are…
Quantitative estimates for a nonlinear inverse source problem in a coupled diffusion equations with uncertain measurements
Chunlong Sun, Wenlong Zhang, Zhidong Zhang
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build…
Determine the point source of the heat equation with sparse boundary measurements
Qiling Gu, Wenlong Zhang, Zhidong Zhang
In this work the authors consider the recovery of the point source in the heat equation. The used data is the sparse boundary measurements. The uniqueness theorem of the inverse pr…
Conditional well-posedness and data-driven method for identifying the dynamic source in a coupled diffusion system from one single boundary measurement
Chunlong Sun, Mengmeng Zhang, Zhidong Zhang
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluoroph…