To the Theory of Diffusion in Inhomogeneous Media: Short Times of the Process

An analytical solution has been obtained for the problem of one-dimensional diffusion in a semiinfinite inhomogeneous medium with an arbitrary dependence of the diffusion coefficient on the distance to the medium boundary for the case of short times of annealing. A numerical comparison of this solution with the known exact solution for a particular case of an exponential dependence of the diffusion coefficient and for the case of a constant coefficient of diffusion has been performed.