A modified method for a backward heat conduction problem

We consider a backward heat conduction problem in a strip, where data is given at the final time t = T(T > 0) and a solution for 0 ⩽ t < T is sought. The problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In order to numerically solve the problem, we study a modification of the equation, where a third-order mixed derivative term is added. Error estimates for this problem are given, which show that the modified problem is stable and its solution is an approximation of the backward heat conduction problem. Some numerical tests illustrate that the proposed method is feasible and effective.