ABSTRACT
In technological and scientific applications related to heat transfer, it is often used to solve the inverse of the heat conduction problem: the so-called backward heat conduction problem (BHCP). This is also called retrospective heat conduction problem, and it is one of the cases in the general classification of inverse heat conduction problems [1]. It is the inverse of the initial boundary value problem for the heat equation; and for this reason, it is also called a final boundary value problem. This problem consists in finding the initial temperature distribution given the final distribution. It is an ill-posed problem since the solution does not have a continuous dependence on the data [2], and it may have no solution at all [3]. Besides this, it is a singular boundary value problem if the domain is unbounded as in the present case. Many methods of solving this problem in bounded domains can be found in the literature; regularization, mollification, and functional methods are popular techniques [4]. Some of these methods may be used together with additional special techniques to treat the case of unbounded domains [5-10].
