Hyperbolic Parabolic Limit, Maxwellian Iteration and Objectivity

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 18 in Rational Extended Thermodynamics beyond the Monatomic Gas, 2015, pp 353-361 from Springer

Abstract: Abstract In this chapter, we discuss the parabolic limit of extended thermodynamics via the Maxwellian iteration, and we observe that the usual constitutive equations, which are nonlocal in space, are approximations of some balance laws of ET when some relaxation times are negligible. An important consequence is that these equations need not satisfy the objectivity principle. To avoid misunderstanding, we should mention that the principle still continues to be valid for constitutive equations. We also discuss the point that, under suitable assumptions, the conditions dictated by the entropy principle in the hyperbolic case guarantee the validity of the entropy principle also in the parabolic limit. Lastly we express our opinion concerning the limitation of the parabolic regularized version of ET theories.

Keywords: Mach Number; Constitutive Equation; Hyperbolic System; Entropy Inequality; Extended Thermodynamic (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_18

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DOI: 10.1007/978-3-319-13341-6_18

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