On repeated concentration and periodic regimes with anomalous diffusion in polymers

D. A. Vorotnikov

Sbornik. Mathematics, Tome 201 (2010) no. 1, pp. 57-77

Résumé

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.

Détail

Keywords: polymer, penetrant, topological degree, weak solution, periodicity.
Mots-clés : non-Fickian diffusion

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