On the uniqueness of the solution to the inverse boundary value problem for the heat equation on a finite time interval

This work is devoted to proving the uniqueness of the solution to the inverse boundary value problem of heat conduction on a finite time interval. For these purposes, the original problem is extended to an infinite time interval, and then the Fourier transform in time is applied to the new problem. As a result, the problem is reduced to a system of ordinary differential equations, which is solved explicitly. A uniqueness theorem is proved for the inverse boundary value problem in Fourier images.