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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 3, Pages 445–472 (Mi zvmmf169)  
This article is cited in 74 scientific papers (total in 75 papers)

Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them

A. A. Zlotnika, B. N. Chetverushkinb

a Department of Applied Mathematics, Russian State Social University, ul. V. Pika 4, Moscow, 129226, Russia
b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
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Abstract: Criteria (necessary and sufficient conditions) for the Petrovskii parabolicity of the quasi-gasdynamic system of equations with an improved description of heat conduction are derived. A modified quasi-gasdynamic system containing second derivatives with respect to both spatial and time variables is proposed. Necessary and sufficient conditions for its hyperbolicity are deduced. For both systems, the stability of small perturbations against a constant background is analyzed and estimates that are uniform on an infinite time interval are given for relative perturbations in the Cauchy problem and the initial-boundary value problem for the corresponding linearized systems. Similar results are also established in the barotropic case with the general equation of state $p=p(\rho)$.
Key words: gas dynamics, quasi-gasdynamic system of equations, second-order parabolic and hyperbolic systems, principal symbol, stability of small perturbations, symmetrization, Fourier transform.
Received: 23.07.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 3, Pages 420–446
DOI: https://doi.org/10.1007/s11470-008-3008-9
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: A. A. Zlotnik, B. N. Chetverushkin, “Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them”, Zh. Vychisl. Mat. Mat. Fiz., 48:3 (2008), 445–472; Comput. Math. Math. Phys., 48:3 (2008), 420–446
Citation in format AMSBIB
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    • This publication is cited in the following 75 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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