On Hyperbolic Pencils for the Grad Moment Systems in Nonequilibrium Thermodynamics

In this paper, we derive sufficient conditions for the stability of a solution to the Cauchy problem of systems of moments of nonequilibrium thermodynamics linearized in the neighborhood of the equilibrium state that are very close to the necessary conditions. The stability conditions are presented in the form of a parametric Hermite theorem for polynomial hyperbolic pencils of any order.__________Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 24, pp. 67–94, 2004.