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

Autor:	Boris N. Chetverushkin, A. A. Zlotnik
Rok vydání:	2008
Předmět:	Computational Mathematics Barotropic fluid Mathematical analysis Symmetrization Initial value problem Constant (mathematics) System of linear equations Thermal conduction Stability (probability) Mathematics Second derivative
Zdroj:	Computational Mathematics and Mathematical Physics. 48:420-446
ISSN:	1555-6662 0965-5425
DOI:	10.1134/s0965542508030081
Popis:	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(ρ).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a77913a6fbe7dd00f3005da0f4d9ab1c https://doi.org/10.1134/s0965542508030081 Zobrazit plný text záznamu Full text from SpringerLink