A monotone iterative reconstruction method for an inverse drift problem in a two-dimensional parabolic equation
Provides a constructive and provably convergent method for an inverse drift problem in parabolic PDEs, which is a specific domain application.
The paper proposes a monotone iterative reconstruction method for recovering the drift coefficient in a 2D parabolic equation from terminal observation data, proving uniqueness and demonstrating effectiveness with numerical experiments including noisy data.
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 observation data $g=u(\cdot,T)$. A monotone operator is constructed whose fixed point coincides with the unknown drift, yielding uniqueness in an admissible class and a constructive iterative reconstruction scheme. Numerical experiments illustrate the monotone convergence and the effectiveness of the proposed method, and show that it remains effective for noisy terminal data under the denoising strategy.