Geodesic
Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 445-472 
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. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 445-472. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a7/
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     title = {Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $p=p(\rho)$.

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