Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Gritsenko S. A. The Global Solvability of the Problem of Nonlinear Diffusion and Slow Convection in Slightly Compressible Viscous Fluid. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2010, vol. 10, iss. 4, pp. 35-41. DOI: 10.18500/1816-9791-2010-10-4-35-41

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.11.2010
Full text:
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Language: 
Russian
Heading: 
Mechanics
UDC: 
517.958:531.72, 517.958:539.3(4)
DOI: 
10.18500/1816-9791-2010-10-4-35-41

The Global Solvability of the Problem of Nonlinear Diffusion and Slow Convection in Slightly Compressible Viscous Fluid

Autors: 
Gritsenko Svetlana Aleksandrovna, Federal State Autonomous Educational Institution of Higher Education ”Belgorod State University”
Abstract: 

The paper deals with Stokes system, corresponding to the motion of slightly compressible viscous fluid where kinematic viscous depends on the admixture concentration. The system also contains the convective diffusion equation. The article proves the existence of generalized solution of the initial-boundary problem for this system in the limited domain with the homogeneous Dirichlet condition for the fluid velocity and the homogeneous Neumann condition for the concentration of admixture on the boundary of domain.

Key words: 
slightly compressible viscous fluid
Stokes equation
convective diffusion equation
References: 
  1. Ладыженская, О.А. Линейные и квазилинейные уравнения параболического типа / О.А. Ладыженская, В.А. Солонников, Н.Н. Уральцева. – М.: Наука, 1967. – 736 c.
  2. Лионс, Ж.-Л. Некоторые методы решения нелинейных краевых задач / Ж.-Л. Лионс. – М.: Мир, 1972. – 588 c.
  3. Треногин, В.А. Функциональный анализ / В.А. Треногин. – М.: Наука, 1980. – 496 с.
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