  Diffusion of a penetrating liquid in a polymeric material does not often
satisfy the classical diffusion equations and requires taking relaxational
(viscoelastic) properties of the polymer into account. We investigate a
boundary value problem on a bounded domain in space for the set of equations
modelling this abnormal diffusion. It is proved that, for any sufficiently
short time segment and any stress prescribed at the beginning of this segment,
there exists a global in time weak solution of the boundary value problem (a
pair: concentration - stress) such that the concentrations at the beginning and
at the end of the segment are the same. Under an additional assumption on
coefficients, existence of time-periodic weak solutions (without any
restrictions of the period length) is shown.
