An Efficient Iteration Method to Reconstruct the Drift Term from the Final Measurement

Abstract.

This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. We construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the uniqueness. The proof of uniqueness contains an iteration converging to the drift, which inspires the numerical algorithm. To handle the ill-posedness of the inverse problem, we add the mollification on the data first in the iterative algorithm and then provide some numerical results.