The inverse problem of finding the time-dependent diffusion coefficient of the heat equation from integral overdetermination data

This article considers the problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional heat equation in the case of nonlocal boundary and integral overdetermination conditions. The conditions for the existence and uniqueness of a classical solution of the problem under considerations are established. A numerical example using the Crank-Nicolson finite-difference scheme combined with an iteration method is presented and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated.