| Issue |
E3S Web Conf.
Volume 234, 2021
The International Conference on Innovation, Modern Applied Science & Environmental Studies (ICIES2020)
|
|
|---|---|---|
| Article Number | 00095 | |
| Number of page(s) | 8 | |
| DOI | https://doi.org/10.1051/e3sconf/202123400095 | |
| Published online | 02 February 2021 | |
On the existence of global solution of the system of equations of liquid movement in porous medium
1 Institute Mathematics and Information Technology, Department of Differential Equations, 656049 Lenina, 61, Barnaul, Russia
2 Lavrentyev Institute of Hydrodynamics SB RAS, 630090 Lavrentieva, 15, Novosibirsk, Russia
* Corresponding author: tma25@ mail.ru
The initial-boundary value problem for the system of one-dimensional isothermal motion of viscous liquid in deformable viscous porous medium is considered. Local theorem of existence and uniqueness of problem is proved in case of compressible liquid. In case of incompressible liquid the theorem of global solvability in time is proved in Holder classes. A feature of the model of fluid filtration in a porous medium considered in this paper is the inclusion of the mobility of the solid skeleton and its poroelastiс properties. The transition from Euler variables to Lagrangian variables is used in the proof of the theorems.
© The Authors, published by EDP Sciences, 2021
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