Spectral Asymptotics of a Linearized Problem Describing Flow of a Viscoelastic Polymeric Fluid.

We study a new rheological model (a modification of a known Pokrovski - Vinogradov model). As was shown by numerical simulations, it takes into account nonlinear effects arising in flows of melts and solutions of polymers in domains with a complex boundary geometry. In the case when the main solution is a Poiseuille-type flow in an infinite plane channel (one considers a viscoelastic polymeric fluid) we obtain an asymptotic formula for the distribution of spectrum points of the linear problem. Small perturbations have such the additional property that they are periodic with respect to the variable going along the side of the channel. [ABSTRACT FROM AUTHOR]