Waves in Hyperbolic Systems

Tommaso Ruggeri and Masaru Sugiyama
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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

Chapter Chapter 3 in Rational Extended Thermodynamics beyond the Monatomic Gas, 2015, pp 55-76 from Springer

Abstract: 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.

Keywords: Shock Wave; Hyperbolic System; Riemann Problem; Shock Structure; Shock Wave Structure (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13341-6_3

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DOI: 10.1007/978-3-319-13341-6_3

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