This article is cited in 35 papers

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

A. A. Zlotnik

Russian State Social University

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.

UDC: 517.958:533.7

Received: 27.07.2007

DOI: 10.4213/mzm4722

 English version: Mathematical Notes, 2008, 83:5, 610–623

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