Recovering the Heat Distribution on the Surface of a Two-dimensional Finite Slab from Interior Data in the Nonhomogeneous Case

Abstract

We considered the two – dimensional problem of reconstructing the historical distribution on the surface of a finite slab from interior temperature data in the nonhomogeneous case. The problem is ill – posed.  So, a regularization is essential. Using the integration truncation method, we have got the estimation of the error between the regularized solution and the exact solution in the nonhomogeneous case. Then, we provided a numerical experiment for illustration ofthe theoretically obtained results.