To the inverse heat conduction problem

An algorithm for the regularization of the inverse heat conduction problem is proposed on the basis of the Fourier method. Unlike many other algorithms, the proposed algorithm does not increase the order of the differential equation. The correctness of the regularized problem is proved and its solution is estimated. A problem of another type is formulated; this problem consists in the determination of sources such that the solution of the resulting boundary value problem asymptotically satisfies the final distribution. This limit problem can be considered as a natural alternative for the inverse problem.