On repeated concentration and periodic regimes with anomalous diffusion in polymers

Spreading of a penetrant in a polymer often disagrees with the classical diffusion equations and requires that relaxation (viscoelastic) properties of polymers be taken into account. We study the boundary-value problem for a system of equations modelling such anomalous diffusion in a bounded space domain. It is demonstrated that for a sufficiently short interval of time and a fixed stress at the beginning of this interval there exists a time-global weak solution of the boundary-value problem (that is, a concentration-stress pair) such that the concentrations at the beginning and the end of the interval of time coincide. Under an additional constraint imposed on the coefficients time-periodic weak solutions (without any limits on the period length) are shown to exist. Bibliography: 28 titles.