Geodesic
Stability criterion for small perturbations for a quasi-gasdynamic system of equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 2, pp. 262-269 Cet article a éte moissonné depuis la source Math-Net.Ru

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The stability of small perturbations against a constant background is studied for a system of quasi-gasdynamic equations in an arbitrary number of space variables. It is established that, for a fixed adiabatic exponent $\gamma$, the stability is determined only by the background Mach number, and a necessary and sufficient condition for stability at any Mach number is $\gamma\le\bar\gamma$, where $\bar\gamma\approx6.2479$. The proof is based on a direct analysis of the corresponding complex characteristic numbers depending on several parameters. The multidimensional case is successfully reduced to the one-dimensional one. Then, the generalized Routh-Hurwitz criterion is applied in conjunction with analytical calculations based on Mathematica. 
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A. A. Zlotnik; I. A. Zlotnik. Stability criterion for small perturbations for a quasi-gasdynamic system of equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 2, pp. 262-269. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_2_a6/

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