On an initial boundary value problem for gas dynamics in thermal nonequilibrium

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Original languageEnglish
Article number121505
Number of pages30
Journal / PublicationJournal of Mathematical Physics
Volume60
Issue number12
Online published10 Dec 2019
Publication statusPublished - Dec 2019

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Abstract

For gas dynamics with several thermal nonequilibrium modes, the global existence of smooth solutions to an initial boundary value problem is established. The key difference compared with the initial value problem studied by Zeng [Arch. Ration. Mech. Anal. 150, 225-279 (1999); ibid. 196, 191-225 (2010)] is the boundary effects, e.g., boundary layers. Moreover, the exponential decay of solutions to an initial boundary value problem of the linearized system with a vibrational nonequilibrium mode is proved via the Fourier analysis, which illustrates a key distinction from that for the initial value problem without a boundary for which the decay is only algebraic.

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