Shock Waves in Hyperbolic Systems of Nonequilibrium Thermodynamics

  • Tommaso RuggeriEmail author
  • Shigeru Taniguchi
Part of the Mathematics of Planet Earth book series (MPE, volume 6)


We present the state of the art of the mathematical theory of shock waves for hyperbolic systems. We start with a brief review of ideal shock waves discussing, in particular, the Riemann problem and the phase transition induced by shock waves in real gases. Then we consider dissipative systems and summarise the results concerning the behaviour of the shock thickness for increasing Mach number . In the last part, we present the framework of Rational Extended Thermodynamics theory of nonequilibrium rarefied gas and its theoretical predictions of shock waves in cases of both monatomic and polyatomic gases. Particular emphasis will be given to subshock formation and the related open problem.


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This work was partially supported by National Group of Mathematical Physics GNFM-INdAM (TR) and by JSPS KAKENHI Grant Number JP16K17555 (ST).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of BolognaBolognaItaly
  2. 2.National Institute of TechnologyKitakyushu CollegeKitakyushuJapan

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