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 Mat. Zametki, 2014, Volume 96, Issue 2, Pages 170–185 (Mi mz10346)

Solvability of the Boundary-Value Problem for Equations of One-Dimensional Motion of a Two-Phase Mixture

I. G. Akhmerova, A. A. Papin

Altai State University, Barnaul

Abstract: For the system of equations of one-dimensional nonstationary motion of a heat-conducting two-phase mixture (of gas and solid particles), the local solvability of the initial boundary value problem is proved. For the case in which the intrinsic densities of the phases are constant and the viscosity and the acceleration of the second phase are small, we establish the “global” (with respect to time) solvability and the convergence (as time increases unboundedly) of the solution of the nonstationary problem to the solution of the stationary one.

Keywords: two-phase mixture of gas and solid particles, nonstationary motion of a two-phase mixture, the maximum principle for concentration and intrinsic density, Reynolds number, Froude number.

DOI: https://doi.org/10.4213/mzm10346

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English version:
Mathematical Notes, 2014, 96:2, 166–179

Bibliographic databases:

UDC: 517.946

Citation: I. G. Akhmerova, A. A. Papin, “Solvability of the Boundary-Value Problem for Equations of One-Dimensional Motion of a Two-Phase Mixture”, Mat. Zametki, 96:2 (2014), 170–185; Math. Notes, 96:2 (2014), 166–179

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz10346
• https://doi.org/10.4213/mzm10346
• http://mi.mathnet.ru/eng/mz/v96/i2/p170

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This publication is cited in the following articles:
1. Vagabov A.I., “n-fold Fourier series expansion in root functions of a differential pencil with n-fold multiple characteristic”, Differ. Equ., 52:5 (2016), 531–537
2. Papin A.A., Tokareva M.A., “Correctness of the Initial-Boundary Problem of the Compressible Fluid Filtration in a Viscous Porous Medium”: A. Chesnokov, E. Pruuel, V. Shelukhin, All-Russian Conference With International Participation Modern Problems of Continuum Mechanics and Explosion Physics Dedicated to the 60th Anniversary of Lavrentyev Institute of Hydrodynamics SB RAS, Journal of Physics Conference Series, 894, IOP Publishing Ltd, 2017, UNSP 012070
3. 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
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