Elliptic and Parabolic Equations - Abstract

Vorotnikov, Dmitry A.

On the system of equations for anomalous diffusion in polymers

We shall consider the system of PDEs which models the non-Fickian anomalous (viscoelastic) diffusion of a penetrant liquid in a polymer. This system belongs to the class which Herbert Amann called `Highly degenerate quasilinear parabolic systems'. We are going to present recent results on existence, uniqueness and attractors for various types of generalized solutions to the corresponding BVPs.
References:
1. H. Amann, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 1991, V. 18, 135-166.
2. D.A. Vorotnikov, J. Math. Anal. Appl., 2008, Volume 339, 876-888.
3. D.A. Vorotnikov, J. Differential Equations, 2009, V. 246, no. 3, 1038-1056.
4. D.A. Vorotnikov, Mat. Sbornik, to appear.
5. D.A. Vorotnikov, In: George Sell Volume, AMS-Fields Communications Series, to appear.
6. D.A. Vorotnikov, In: Differential Equations: Systems, Applications and Analysis, F. Columbus (ed.), Nova Science, in print.