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Matematicheskie Zametki, 2008, Volume 83, Issue 5, Pages 667–682
DOI: https://doi.org/10.4213/mzm4722 (Mi mzm4722) 		 
This article is cited in 35 scientific papers (total in 35 papers)

Parabolicity of a Quasihydrodynamic System of Equations and the Stability of its Small Perturbations

A. A. Zlotnik

Russian State Social University
Full-text PDF (523 kB) Citations (35)
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DOI: https://doi.org/10.4213/mzm4722
Abstract: 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.
Keywords: quasihydrodynamic system of equations, Petrovskii parabolic system, stability of small perturbations, Cauchy problem, perfect polytropic gas, barotropic system.
Received: 27.07.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 5, Pages 610–623
DOI: https://doi.org/10.1134/S0001434608050040
Bibliographic databases:
UDC: 517.958:533.7
Language: Russian
Citation: A. A. Zlotnik, “Parabolicity of a Quasihydrodynamic System of Equations and the Stability of its Small Perturbations”, Mat. Zametki, 83:5 (2008), 667–682; Math. Notes, 83:5 (2008), 610–623
Citation in format AMSBIB
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    • This publication is cited in the following 35 articles:
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