Аннотация
We consider the problem of modeling the process of determining the distribution function of temperature and time varying structure of homogeneous bar of a given law changes in the average temperature. So there is an inverse problem for the heat equation in which together with finding the solution of the equation it is required to find unknown coefficient depending only on the time variable. The specific features of the considered problems is that the system of eigenfunctions of the multiple differentiation operator subject to boundary conditions of the initial problem does not have the basis property. In this paper, it is proved that this inverse problem has a unique generalized solution.