Geodesic
Parabolicity of a Quasihydrodynamic System of Equations and the Stability of its Small Perturbations
Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 667-682

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We establish that the quasihydrodynamic system of equations of motion of a perfect polytropic gas is parabolic (in the sense of Petrovskii). We study the stability of small perturbations on a constant background and, for the Cauchy problem and the initial boundary-value problems for the corresponding linearized system, we obtain uniform (on the infinite time interval) estimates of relative perturbations. The corresponding results are also derived in the barotropic case for a general equation of state.
Mots-clés : quasihydrodynamic system of equations
Keywords: Petrovskii parabolic system, stability of small perturbations, Cauchy problem, perfect polytropic gas, barotropic system. 
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     author = {A. A. Zlotnik},
     title = {Parabolicity of a {Quasihydrodynamic} {System} of {Equations} and the {Stability} of its {Small} {Perturbations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {667--682},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a3/}
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A. A. Zlotnik. Parabolicity of a Quasihydrodynamic System of Equations and the Stability of its Small Perturbations. Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 667-682. http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a3/