The source control in the problem of heat conduction

For the heat conduction equation, a boundary value problem that consists in determining the density of volume sources which provides a prescribed final ($T>0$) temperature distribution is considered. The correctness of the problem is proved, a convergent algorithm is constructed, and an algorithm for solving the inverse problem of heat conduction is proposed. The work was performed in the framework of the target program (project 2.1.1/1292) and was supported by the Russian Foundation for Basic Research (projects 11-01-96511a and 13-01-00096a).