The truncation method for a two-dimensional nonhomogeneous backward heat problem

摘要

We consider the backward heat problemwith the homogeneous Dirichlet condition on the rectangle Ω = (0, π) × (0, π), where the data f and g are given approximately. The problem is severely ill-posed. Using the truncation method for Fourier series we propose a simple regularized solution which not only works on a very weak condition on the exact data but also attains, due to the smoothness of the exact solution, explicit error estimates which include the approximation in H2(Ω). Some numerical examples are given to illuminate the effect of our method.