A. A. Papin, I. G. Akhmerova, “Solvability of the System of Equations of One-Dimensional Motion of a Heat-Conducting Two-Phase Mixture”, Mat. Zametki, 87:2 (2010), 246–261; Math. Notes, 87:2 (2010), 230

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Matematicheskie Zametki, 2010, Volume 87, Issue 2, Pages 246–261
DOI: https://doi.org/10.4213/mzm7706 (Mi mzm7706)

This article is cited in 17 scientific papers (total in 17 papers)

Solvability of the System of Equations of One-Dimensional Motion of a Heat-Conducting Two-Phase Mixture

A. A. Papin, I. G. Akhmerova

Altai State University

Full-text PDF (527 kB) Citations (17)

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DOI: https://doi.org/10.4213/mzm7706

Abstract: We prove the local solvability of the initial boundary-value problem for the system of equations of one-dimensional nonstationary motion of a heat-conducting two-phase mixture (gas plus solid particles). For the case in which the real densities of the phases are constant, we establish the solvability “in the large” with respect to time.

Keywords: motion of a heat-conducting two-phase mixture, quasilinear system of equations, viscous gas, Lebesgue space, Hölder space, Lagrangian variable, Cauchy problem, parabolic equation, Tikhonov–Schauder theorem, incompressible medium.

Received: 17.02.2009
Revised: 14.06.2009

English version:
Mathematical Notes, 2010, Volume 87, Issue 2, Pages 230–243
DOI: https://doi.org/10.1134/S0001434610010293

Bibliographic databases:

UDC: 517.946

Language: Russian

Citation: A. A. Papin, I. G. Akhmerova, “Solvability of the System of Equations of One-Dimensional Motion of a Heat-Conducting Two-Phase Mixture”, Mat. Zametki, 87:2 (2010), 246–261; Math. Notes, 87:2 (2010), 230–243

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm7706

https://doi.org/10.4213/mzm7706

https://www.mathnet.ru/eng/mzm/v87/i2/p246

This publication is cited in the following 17 articles:

A. E. Mamontov, D. A. Prokudin, “Asymptotic Behavior of the Solution to the Initial-boundary Value Problem for One-dimensional Motions of a Barotropic Compressible Viscous Multifluid”, Lobachevskii J Math, 45:4 (2024), 1463
D.A. Prokudin, “Stabilization of the Solution to the Initial-Boundary Value Problem for One-Dimensional Isothermal Equations of Viscous Compressible Multicomponent Media”, Izvestiya AltGU, 2023, no. 4(132), 73
Dmitriy Prokudin, “On the Stabilization of the Solution to the Initial Boundary Value Problem for One-Dimensional Isothermal Equations of Viscous Compressible Multicomponent Media Dynamics”, Mathematics, 11:14 (2023), 3065
I.G. Akhmerova, A.V. Ustyuzhanova, “Numerical solution of a boundary value problem for one-dimensional motion of a granular matter”, Yuzhno-Sibirskii nauchnyi vestnik, 2023, no. 4(50), 72
I.G. Akhmerova, A.S. Pravdivtsev, “Local Solvability of a Boundary Value Problem for One-Dimensional Motion of a Granular Matter”, Izvestiya AltGU, 2023, no. 4(132), 59
I.G. Akhmerova, “Local Solvability of the Flow Problem for the Equations of Motion of Two Interpene Crating Fluids”, Izvestiya AltGU, 2022, no. 1(123), 73
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. elektron. matem. izv., 18:2 (2021), 1397–1422
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
Miglena N. Koleva, Lubin G. Vulkov, Studies in Computational Intelligence, 961, Advanced Computing in Industrial Mathematics, 2021, 222
Alexander A. Papin, Margarita A. Tokareva, Rudolf A. Virts, “Filtration of liquid in a non-isothermal viscous porous medium”, Zhurn. SFU. Ser. Matem. i fiz., 13:6 (2020), 763–773
Koleva M.N., Vulkov L.G., “Numerical Analysis of One Dimensional Motion of Magma Without Mass Forces”, J. Comput. Appl. Math., 366 (2020), UNSP 112338
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”, J. Appl. Industr. Math., 13:2 (2019), 350–362
Alexander A. Papin, Margarita A. Tokareva, “On local solvability of the system of the equations of one dimensional motion of magma”, Zhurn. SFU. Ser. Matem. i fiz., 10:3 (2017), 385–395
M A Tokareva, “Solvability of initial boundary value problem for the equations of filtration in poroelastic media”, J. Phys.: Conf. Ser., 722 (2016), 012037
I. G. Akhmerova, A. A. Papin, “Solvability of the Boundary-Value Problem for Equations of One-Dimensional Motion of a Two-Phase Mixture”, Math. Notes, 96:2 (2014), 166–179
Irina G. Akhmerova, “Razreshimost kraevoi zadachi dlya uravnenii odnomernogo dvizheniya dvukhfaznoi smesi”, Zhurn. SFU. Ser. Matem. i fiz., 5:1 (2012), 25–35
Papin A.A., Tokareva M.A., “Zadacha o dvizhenii szhimaemoi zhidkosti v deformiruemoi poristoi srede”, Izvestiya Altaiskogo gosudarstvennogo universiteta, 2011, no. 1-2, 36–43

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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