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

I. G. Akhmerova; A. A. Papin

Geodesic

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

I. G. Akhmerova ; A. A. Papin

Matematičeskie zametki, Tome 96 (2014) no. 2, pp. 170-185

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Résumé

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.

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     author = {I. G. Akhmerova and A. A. Papin},
     title = {Solvability of the {Boundary-Value} {Problem} for {Equations} of {One-Dimensional} {Motion} of a {Two-Phase} {Mixture}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {96},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_2_a1/}
}

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I. G. Akhmerova; A. A. Papin. Solvability of the Boundary-Value Problem for Equations of One-Dimensional Motion of a Two-Phase Mixture. Matematičeskie zametki, Tome 96 (2014) no. 2, pp. 170-185. http://geodesic.mathdoc.fr/item/MZM_2014_96_2_a1/