  We consider an inhomogeneous initial-boundary value problem for a Petrovskii
parabolic system of second order PDEs. We prove that this problem induces
isomorphisms between appropriate anisotropic generalized Sobolev spaces. The
regularity of these spaces are given by a pair of real numbers and by a
function parameter. The latter allows us to characterize the regularity of
solutions to the problem more finely as compared with anisotropic Sobolev
spaces.
