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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 2, Pages 1397–1422
DOI: https://doi.org/10.33048/semi.2021.18.106 (Mi semr1447) 		 
Differentical equations, dynamical systems and optimal control

On the existence of global solution of the system of equations of one-dimensional motion of a viscous liquid in a deformable viscous porous medium

M. A. Tokareva, A. A. Papin

Altai State University, 61, Lenina ave., Barnaul, 656049, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.106
Abstract: The initial-boundary value problem for the system of one-dimensional motion of a viscous liquid in a deformable viscous porous medium is considered. Local theorem of existence and uniqueness of the problem is proved in the case of compressible liquid. In the case of incompressible liquid the theorem of global solvability in time is proved in Holder classes.
Keywords: Darcy's law, poroelasticity, filtration, global solvability, porosity.
Funding agency Grant number
Russian Science Foundation 19-11-00069
The work of the first author is supported by the Russian Science Foundation (Project No. 19-11-00069).
Received August 16, 2021, published November 26, 2021
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 76S05, 35Q74, 35Q35, 35G31
Language: English
Citation: M. A. Tokareva, A. A. Papin, “On the existence of global solution of the system of equations of one-dimensional motion of a viscous liquid in a deformable viscous porous medium”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1397–1422
Citation in format AMSBIB
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\by M.~A.~Tokareva, A.~A.~Papin
\paper On the existence of global solution of the system of equations of one-dimensional motion of a viscous liquid in a deformable viscous porous medium
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 2
\pages 1397--1422
\mathnet{http://mi.mathnet.ru/semr1447}
\crossref{https://doi.org/10.33048/semi.2021.18.106}
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