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

This article is cited in 3 scientific papers (total in 3 papers)

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

Full text: PDF file (514 kB)
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English version:
Mathematical Notes, 2014, 96:2, 166–179

Bibliographic databases:

UDC: 517.946
Received: 12.07.2013

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  crossref  mathscinet  zmath  isi  elib  scopus
    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  crossref  isi  scopus
    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  mathnet  crossref
  • Математические заметки Mathematical Notes
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