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Waves in Hyperbolic Systems

In: Rational Extended Thermodynamics beyond the Monatomic Gas

Author

Listed:
  • Tommaso Ruggeri

    (University of Bologna, Dept. of Mathematics and Res. Center of Applied Mathematics AM²)

  • Masaru Sugiyama

    (Nagoya Institute of Technology, Graduate School of Engineering)

Abstract

Wave propagation phenomena give us an important mean to check the validation of the 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). The chapter finishes with the discussion of traveling waves, in particular, shock waves with structure. The sub-shock formation is particularly interesting. The Riemann problem and the large time asymptotic behavior are also discussed.

Suggested Citation

  • Tommaso Ruggeri & Masaru Sugiyama, 2015. "Waves in Hyperbolic Systems," Springer Books, in: Rational Extended Thermodynamics beyond the Monatomic Gas, edition 1, chapter 0, pages 55-76, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13341-6_3
    DOI: 10.1007/978-3-319-13341-6_3
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