Stability Results for an Inverse Parabolic Problem

Abstract

In this paper, a one dimensional inverse parabolic problem in a quarter plane will be considered. The unknown function in a boundary is estimated from an over specified condition at a fixed location inside the region by solving an illposed integral equation. The Tikhonov Regularization method of the 1st order is applied in order to stabilize the solution of the ill-posed problem. The solution of the inverse problem is defined by minimization of the Tikhonov functional. Some analytical results for regularization parameter determination and stability of solution of inverse problem are derived.