An optimal modified method for a two-dimensional inverse heat conduction problem

We consider a two-dimensional inverse heat conduction problem which is severely ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. From the frequency domain, we propose an optimal modified method to solve the problem in the presence of noisy data. We give and prove the optimal convergence estimate, which shows that the regularized solution is dependent continuously on the data and is an approximation of the exact solution of the two-dimensional inverse heat conduction problem.