7 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…
Solving the inverse Source Problems for wave equation with final time measurements by a data driven approach
Qiling Gu, Wenlong Zhang, Zhidong Zhang
This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the -Tikhonov regular…
A Data-Driven Approach to Solving First-Kind Fredholm Integral Equations and Their Convergence Analysis
Duan-Peng Ling, Wenlong Zhang
We investigate the statistical recovery of solutions to first-kind Fredholm integral equations with discrete, scattered, and noisy pointwise measurements. Assuming the forward oper…
Stochastic Convergence Analysis of Inverse Potential Problem
Bangti Jin, Qimeng Quan, Wenlong Zhang
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling…
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…