Abstract:
The mathematical statement is given for the problem of filtration of a viscous fluid in a deformable porous medium that possesses predominantly viscous properties. Some theorems are proved on local solvability and existence of a global-in-time solution in the Hölder classes for the problem.
Keywords:
Darcy law, poroelasticity, filtration, global solvability, uniqueness.
Citation:
M. A. Tokareva, A. A. Papin, “Global solvability of a system of equations of one-dimensional motion of a viscous fluid in a deformable viscous porous medium”, Sib. Zh. Ind. Mat., 22:2 (2019), 81–93; J. Appl. Industr. Math., 13:2 (2019), 350–362
\Bibitem{TokPap19}
\by M.~A.~Tokareva, A.~A.~Papin
\paper Global solvability of a system of equations of one-dimensional motion of a viscous fluid in a deformable viscous porous medium
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 2
\pages 81--93
\mathnet{http://mi.mathnet.ru/sjim1045}
\crossref{https://doi.org/10.33048/sibjim.2019.22.208}
\elib{https://elibrary.ru/item.asp?id=41641475}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 2
\pages 350--362
\crossref{https://doi.org/10.1134/S1990478919020169}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067309726}
Linking options:
https://www.mathnet.ru/eng/sjim1045
https://www.mathnet.ru/eng/sjim/v22/i2/p81
This publication is cited in the following 15 articles:
Rudolf Aleksandrovich Virts, “Osesimmetrichnaya zadacha filtratsii gaza v porouprugoi srede”, Comp. Contin. Mech., 17:4 (2025), 496
P. V. Gilev, A. A. Papin, “Filtration of two immiscible incompressible fluids”, J. Appl. Industr. Math., 18:2 (2024), 234–245
E. Sh. Nazirova, A. Nematov, I. M. Nabiyev, M. E. Shukurova, I. Tanaino, T. Dzholdosheva, “Construction of a numerical model and algorithm for solving two-dimensional problems of filtration of multicomponent liquids, taking into account the moving “oil-water” interface”, E3S Web of Conf., 402 (2023), 14040
Rudolf Virts, Margarita Tokareva, Konstantin Shishmarev, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 020009
P.V. Gilev, A.A. Papin, “Existence of a Weak Solutionto the Two-Dimensional Filtration Problem in a Thin Poroelastic Layer”, Izvestiya AltGU, 2022, no. 4(126), 93
Miglena N. Koleva, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 080023
A. A. Papin, M. A. Tokareva, “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. Electron. Math. Rep., 18:2 (2021), 1397–1422
A. A. Papin, M. A. Tokareva, “Mathematical Model of Fluids Motion in Poroelastic Snow-Ice Cover”, J. Sib. Fed. Univ.-Math. Phys., 14:1 (2021), 47–56
Margarita Tokareva, Alexander Papin, S. Bourekkadi, J. Abouchabaka, O. Omari, K. Slimani, “On the existence of global solution of the system of equations of liquid movement in porous medium”, E3S Web Conf., 234 (2021), 00095
R.A . Virts, “Numerical Solution of One Problem of Carbon Dioxide Injection into the Rock”, Izvestiya AltGU, 2021, no. 4(120), 81
R.A. Virts, “Numerical Solution of a Two-Dimensional Problem of Fluid Filtration in a Deformable Porous Medium”, Izvestiya AltGU, 2021, no. 1(117), 88
A. A. Papin, M. A. Tokareva, R. A. Virts, “Filtration of Liquid in a Non-Isothermal Viscous Porous Medium”, J. Sib. Fed. Univ.-Math. Phys., 13:6 (2020), 763–773
M.A. Tokareva, “On Global Solvability of a Problem of a Viscous Liquid Motion in a Deformable Viscous Porous Medium”, Izvestiya AltGU, 2020, no. 1(111), 133
R.A. Virts, A.A. Papin, W.A. Weigant, “Numerical Solotion of a Problem of Fluid Filtration in a Viscoelastic Porous Medium”, Izvestiya AltGU, 2020, no. 1(111), 72
R Virts, A Papin, M Tokareva, “Non-isothermal filtration of a viscous compressible fluid in a viscoelastic porous medium”, J. Phys.: Conf. Ser., 1666:1 (2020), 012041
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