7 papers · 1 filter
Error Analysis of the Inverse Conductivity Problem with Scattered Measurements
Bangti Jin, Qimeng Quan, Wenlong Zhang
In this work, we investigate the inverse problem of recovering the conductivity coefficient in an elliptic equation from noisy measurements collected at finitely many deterministic…
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…
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…
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…
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…