On the stabilization of solutions to the initial-boundary value problem for the equations of dynamics of viscous compressible multicomponent media
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1278-1285.

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An initial-boundary value problem for one-dimensional equations of the dynamics of viscous compressible multicomponent media is considered, and the viscosity matrix is not assumed to be diagonal. The stabilization of the solution to the initial-boundary value problem with an unlimited increase of time is proved.
Keywords: compressible viscous medium, multicomponent flows, stabilization of solution.
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D. A. Prokudin. On the stabilization of solutions to the initial-boundary value problem for the equations of dynamics of viscous compressible multicomponent media. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1278-1285. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a49/

[1] A.V. Kazhikhov, “Stabilization of solutions of an initial-boundary-value problem for the equations of motion of a barotropic viscous fluid”, Differ. Equations, 15:4 (1979), 463–467 | Zbl

[2] I. Straskraba, “Recent progress in the mathematical theory of 1D barotropic flow”, Ann. Univ. Ferrara, Sez. VII, Sci. Mat., 55:2 (2009), 395–405 | DOI | Zbl

[3] I. Straskraba, 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 | Zbl

[4] I. Straskraba, 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 | Zbl

[5] A.A. Zlotnik, Nguen Zha Bao, “The behavior as $t\rightarrow +\infty$ of solutions to a quasilinear nonstationary problem with free boundaries”, Differ. Equations, 30:6 (1994), 1003–1005 | Zbl

[6] A.A. Zlotnik, “Stabilization of solutions of a certain quasilinear system of equations with a weakly monotone nonlinearity”, Differ. Equations, 35:10 (1999), 1423–1428 | Zbl

[7] A.A. Zlotnik, “Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations”, Differ. Equations, 36:5 (2000), 701–716 | DOI | Zbl

[8] 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 | Zbl

[9] 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 | DOI | Zbl

[10] 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 | Zbl

[11] 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. Physics: Conference Series, 894 (2017), 012076 | DOI