Compressible Euler equations with second sound: Asymptotics of discontinuous solutions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:401

Article

Fang, Beixiang¹  Racke, Reinhard² 

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Univ Konstanz, Dept Math & Stat, D-78457 Constance, Germany

关键词: Discontinuous solutions;    Asymptotic behavior;    Curvature;    Hyperbolic heat conduction;   

DOI  :  10.1016/j.jmaa.2012.10.068

来源: Elsevier

【 摘 要 】

We consider the compressible Euler equations in three space dimensions where heat conduction is modeled by Cattaneo's law instead of Fourier's law. For the arising purely hyperbolic system, the asymptotic behavior of discontinuous solutions to the linearized Cauchy problem is investigated. We give a description of the behavior as time tends to infinity and, in particular, as the relaxation parameter tends to zero. The latter corresponds to the singular limit and a formal convergence to the classical (i.e. Fourier law for the heat flux-temperature relation) Euler system. We recover, a phenomenon observed for hyperbolic thermoelasticity, namely the dependence of the asymptotic behavior on the mean curvature of the initial surface of discontinuity; in addition, we observe a more complex behavior in general. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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