Mikhail A. Artemov, Evgenii S. Baranovskii
Abstract:
We study the mixed boundary-value problem for steady motion equations of an
incompressible viscoelastic medium of Jeffreys type in a fixed three-dimensional
domain. On one part of the boundary the no-slip condition is provided,
while on the other one the impermeability condition and non-homogeneous
Dirichlet boundary conditions for tangential component of the surface force
is used. The existence of weak solutions of the formulated boundary-value problem
is proved. Some estimates for weak solutions are established; it is shown
that the set of weak solutions is sequentially weakly closed.
Submitted June 17, 2015. Published September 29, 2015.
Math Subject Classifications: 35Q35, 35D30.
Key Words: Mixed boundary-value problems; weak solutions; existence theorem;
viscoelastic medium.
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Mikhail A. Artemov Department of Applied Mathematics, Informatics and Mechanics Voronezh State University 394006 Voronezh, Russia email: artemov_m_a@mail.ru |
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Evgenii S. Baranovskii Department of Applied Mathematics, Informatics and Mechanics Voronezh State University 394006 Voronezh, Russia email: esbaranovskii@gmail.com |
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