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Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation. (English) Zbl 0966.76079
Author’s abstract: We study gas flow in vibrational nonequilibrium. The model is a $$4\times 4$$ nonlinear hyperbolic system with relaxation. Under physical assumptions, properties of thermodynamic variables relevant to stability are obtained, global existence for Cauchy problems with smooth and small data is established, and large-time behavior is studied in the pointwise sense. We find the fundamental solution in a systematic way for a general linear system with relaxation. The fundamental solution provides insight into the behavior of the nonlinear system, and is crucial to obtain our pointwise asymptotic picture for the nonequilibrium flow. We also clarify in a general setting the relation between subcharacteristic conditions and a dissipative criterion that was originally proposed for hyperbolic-parabolic systems and has now proved to be important also for hyperbolic systems with relaxation.

##### MSC:
 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35L65 Hyperbolic conservation laws
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