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Waves in Hyperbolic Systems

In: Classical and Relativistic Rational Extended Thermodynamics of Gases

Author

Listed:
  • Tommaso Ruggeri

    (University of Bologna, Department of Mathematics and Research Center on Applied Mathematics)

  • Masaru Sugiyama

    (Nagoya Institute of Technology)

Abstract

Wave propagation phenomena give us an important mean to check the validation of a nonequilibrium thermodynamics theory. In this chapter, we present a short review on the modern theory of wave propagation for hyperbolic systems. Firstly, we present the theory of linear waves emphasizing the role of the dispersion relation. The high frequency limit in the dispersion relation is also studied. Secondly, nonlinear acceleration waves are discussed together with the transport equation and the critical time. Thirdly, we present the main results concerning shock waves as a particular class of weak solutions and the admissibility criterion to select physical shocks (Lax condition, entropy growth condition, and Liu condition). Fourth, we discuss traveling waves, in particular, shock waves with structure. The subshock formation is particularly interesting. The Riemann problem and the problem of the large-time asymptotic behavior are also discussed. Lastly, we present toy models to show explicitly some interesting features obtained here.

Suggested Citation

  • Tommaso Ruggeri & Masaru Sugiyama, 2021. "Waves in Hyperbolic Systems," Springer Books, in: Classical and Relativistic Rational Extended Thermodynamics of Gases, chapter 0, pages 67-106, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-59144-1_3
    DOI: 10.1007/978-3-030-59144-1_3
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