Stationary solutions of a boundary value problem for equations of barotropic flow of multicomponent media
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1490-1498.

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The asymptotic behavior (as $t\rightarrow +\infty$) of the solution to the initial-boundary value problem is analyzed for the system of differential equations describing the barotropic dynamics of a viscous  multifluid with a non-diagonal, symmetric and positive definite viscosity matrix, in the case of one spatial variable. New a priori estimates are obtained and stabilization of the solution to the initial-boundary value problem is proved.
Keywords: barotropic flow, viscosity matrix, stabilization of solution.
Mots-clés : viscous compressible multifluid
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A. E. Mamontov; D. A. Prokudin. Stationary solutions of a boundary value problem for equations of barotropic flow of multicomponent media. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1490-1498. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a49/

[1] A.E. Mamontov, D.A. Prokudin, “Viscous compressible homogeneous multi-fluids with multiple velocities: barotropic existence theory”, Sib. Èlectron. Math. Izv., 14 (2017), 388–397 | DOI | MR | Zbl

[2] A.A. Zlotnik, B. Ducomet, “Stabilization rate and stability for viscous compressible barotropic symmetric flows with free boundary for a general mass force”, Sb. Math., 196:12 (2005), 1745–1799 | DOI | MR | Zbl

[3] I. Straškraba, A. Zlotnik, “Global properties of solutions to 1D-viscous compressible barotropic fluid equations with density dependent viscosity”, Z. Angew. Math. Phys., 54:4 (2003), 593–607 | DOI | MR | Zbl

[4] I. Straškraba, A. Zlotnik, “Global behavior of 1d-viscous compressible barotropic fluid with a free boundary and large data”, J. Math. Fluid Mech., 5:2 (2003), 119–143 | DOI | MR | Zbl

[5] A.A. Zlotnik, “On equations for one-dimensional motion of a viscous barotropic gas in the presence of a body force”, Sib. Math. J., 33:5 (1992), 798–815 | DOI | MR | Zbl

[6] S.N. Antontsev, A.V. Kazhikhov, V.N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids, Studies in Mathematics and its Applications, 22, North-Holland, Amsterdam etc., 1990 | DOI | MR | Zbl

[7] A.V. Kazhikhov, “Stabilization of solutions of the initial-boundary value problem for barotropic viscous fluid equations”, Differ. Uravn., 15:4 (1979), 662–667 | MR | Zbl

[8] D.A. 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 | DOI | MR

[9] D.A. Prokudin, “On the stabilization of solutions to the initial-boundary value problem for the equations of dynamics of viscous compressible multicomponent media”, Sib. Èlectron. Math. Izv., 18:2 (2021), 1278–1285 | DOI | MR | Zbl

[10] A.E. Mamontov, D.A. Prokudin, “Global unique solvability of the initial-boundary value problem for the equations of one-dimensional polytropic flows of viscous compressible multifluids”, J. Math. Fluid Mech., 21:1 (2019), 9 | DOI | MR | Zbl

[11] A.E. Mamontov, D.A. Prokudin, “Unique solvability of initial-boundary value problem for one-dimensional equations of polytropic flows of multicomponent viscous compressible fluids”, Sib. Èlectron. Math. Izv., 15 (2018), 631–649 | DOI | MR | Zbl

[12] D.A. Prokudin, “Unique solvability of initial-boundary value problem for a model system of equations for the polytropic motion of a mixture of viscous compressible fluids”, Sib. Èlectron. Math. Izv., 14 (2017), 568–585 | DOI | MR | Zbl

[13] D.A. Prokudin, “Global solvability of the initial boundary value problem for a model system of one-dimensional equations of polytropic flows of viscous compressible fluid mixtures”, J. Phys.: Conf. Ser., 894 (2017), 012076 | DOI | MR

[14] A.E. Mamontov, D.A. Prokudin, “Global unique solvability of an initial-boundary value problem for the one-dimensional barotropic equations of binary mixtures of viscous compressible fluids”, J. Appl. Ind. Math., 15:1 (2021), 50–61 | DOI | MR | Zbl

[15] S. Li, “On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains”, Z. Angew. Math. Phys., 68:5 (2017), 106 | DOI | MR | Zbl

[16] D. Bresch, X. Huang, J. Li, “Global weak solutions to one-dimensional non-conservative viscous compressible two-phase system”, Commun. Math. Phys., 309:3 (2012), 737–755 | DOI | MR | Zbl

[17] A.A. Papin, “On the uniqueness of the solutions of an initial boundary-value problem for the system of a heat-conducting two-phase mixture”, Math. Notes, 87:4 (2010), 594–598 | DOI | MR | Zbl

[18] A.A. Zlotnik, “Weak solutions to the equations of motion of viscous compressible reacting binary mixtures: Uniqueness and Lipschitz-continuous dependence on data”, Math. Notes, 75:2 (2004), 278–283 | DOI | MR | Zbl

[19] A.A. Zlotnik, “Uniform estimates and stabilization of solutions to equations of one-dimensional motion of a multicomponent barotropic mixture”, Math. Notes, 58:2 (1995), 885–889 | DOI | MR | Zbl

[20] A.N. Petrov, “Well-posedness of initial-boundary value problems for one-dimensional equations of mutually penetrating flows of ideal gases”, Din. Splosh. Sredy, 56 (1982), 105–121 | MR

[21] A.V. Kazhikov, A.N. Petrov, “Well-posedness of the initial-boundary value problem for a model system of equations of a multicomponent mixture”, Din. Splosh. Sredy, 35 (1978), 61–73 | MR