This article is cited in 13 papers

Phase space of the initial-boundary value problem for the Oskolkov system of nonzero order

A. O. Kondyukov, T. G. Sukacheva

Novgorod State University, ul. Bol’shaya Sankt-Peterburgskaya 41, Novgorod the Great, 173003, Russia

Abstract: The phase space of the Dirichlet initial-boundary value problem for a system of partial differential equations modeling the flow of an incompressible viscoelastic Kelvin–Voigt fluid of nonzero order is described. The investigation is based on the theory of semilinear Sobolev-type equations and the concepts of a relatively spectral bounded operator and a quasi-stationary trajectory for the corresponding Oskolkov system modeling the plane-parallel flow of the above fluid.

Key words: Sobolev-type equations, phase space, quasi-stationary trajectories, Oskolkov system, incompressible viscoelastic Kelvin–Voigt fluid.

UDC: 519.63

MSC: Primary 35Q35; Secondary 76A10

Received: 19.09.2014

DOI: 10.7868/S0044466915050130

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:5, 823–828

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