Regularization of the backward stochastic heat conduction problem

Abstract

In this paper, we study the backward problem for the stochastic parabolic heat equation driven by a Wiener process. We show that the problem is ill-posed by violating the continuous dependence on the input data. In order to restore stability, we apply a filter regularization method which is completely new in the stochastic setting. Convergence rates are established under different a priori assumptions on the sought solution.

On recovering the source term for the heat equation with memory term

“…-If m = 0 the problem (1.1) is called classical parabolic equation. This problem has been studied a lot in [9,11,10,2,18,20,12,22,21,5,17,19,14,13].…”