On the Classicality of Solutions to a Boundary Value Problem for a Second-Order Parabolic System

We study a parabolic initial-boundary-value problem for a system of two differential equations with two boundary conditions of different orders, the Dirichlet and Neumann ones. It occurs specifically in the heat-mass transfer theory. We find sufficient conditions for the generalized solution of the problem to be classical. They are formulated in terms of the belonging of the problem data to generalized anisotropic Sobolev spaces.