UDC 517.9 ON THE INITIAL-BOUNDARY VALUE PROBLEM FOR EQUATIONS OF ANOMALOUS DIFFUSION IN POLYMERS D. A. Vorotnikov* Voronezh State University We study the system of partial differential equations which describes the diffusion of a penetrant liquid in a polymer. <...> We construct weak solutions to the initial-boundary value problem for this system in a bounded domain. <...> KEY WORDS: anomalous diffusion, polymer—penetrant systems, topological degree, weak solution, nonlinear PDE. 1. <...> INTRODUCTION It is well known that diffusion in continuums is described by the following conservation law: ∂ ∂ =-u t where uut x=, JJ t x=, div J (1.1) () is the concentration and () is the concentration flux vector (they depend on time t and the spatial point x ). <...> The first one is so-called “case II diffusion” where concentration fronts can move with constant speed (the Fick’s law implies that a front should propagate with speed proportional to 1 one is called “sorption overshoot”. <...> It means that the mass of penetrant absorbed by the polymer increases sharply until some point and then deThe work was partially supported by BRHE Program of Ministry of Education and Science of Russia and CRDF and by RFBR N 07-01-00137. © Vorotnikov D. A. , 2008 * t ). <...> One of such relations (based on the relaxation (viscoelastic) mechanism) was proposed by Cohen et al. [3,4] for the diffusion of a penetrant liquid in a polymer: JDu=- — - () u -— , К Eu ЪЪ u x d f u s x us x t Л Б () exp ( ( ))bx x˜ -• t s ,, b ˆ ¯ К Л Б ,,∂, ∂s ( ) () ˆ ¯ ˜ ds. (1.5) Here ED are functions of a scalar argument, f is a scalar function of two scalar arguments, D and E are called the diffusion and stress-diffusion coefficients, respectively. <...> H. Amann [2] considers a wide class of these particular cases and shows existence of maximal (not global in time) solutions. <...> A global existence result is given in [7] but under additional conditions on initial and boundary data. <...> It is formulated for 01, but << = m and x the technique used there seems to be applicable <...>