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This article is cited in 7 scientific papers (total in 7 papers)
Review Articles
On a class of Sobolev-type equations
T. G. Sukacheva, A. O. Kondyukov Novgorod State University, Velikiy Novgorod, Russian Federation
Abstract:
The article surveys the works of T. G. Sukacheva and her students studying the models of incompressible viscoelastic Kelvin–Voigt fluids in the framework of the theory of semilinear Sobolev-type equations. We focus on the unstable case because of greater generality. The idea is illustrated by an example: the non-stationary thermoconvection problem for the order 0 Oskolkov model. Firstly, we study the abstract Cauchy problem for a semilinear nonautonomous Sobolev-type equation. Then, we treat the corresponding initial-boundary value problem as its concrete realization. We prove the existence and uniqueness of a solution to the stated problem. The solution itself is a quasi-stationary semi-trajectory. We describe the extended phase space of the problem. Other problems of hydrodynamics can also be investigated in this way: for instance, the linearized Oskolkov model, Taylor's problem, as well as some models describing the motion of an incompressible viscoelastic Kelvin–Voigt fluid in the magnetic field of the Earth.
Keywords:
Sobolev type equations; incompressible viscoelastic fluids; relatively $p$-sectorial operators; extended phase spaces.
Received: 15.09.2014
Citation:
T. G. Sukacheva, A. O. Kondyukov, “On a class of Sobolev-type equations”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:4 (2014), 5–21
Linking options:
https://www.mathnet.ru/eng/vyuru234 https://www.mathnet.ru/eng/vyuru/v7/i4/p5
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Abstract page: | 261 | Full-text PDF : | 118 | References: | 57 |
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