Hyperbolic Parabolic Limit, Maxwellian Iteration, and Objectivity

Tommaso Ruggeri and Masaru Sugiyama
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Tommaso Ruggeri: University of Bologna, Department of Mathematics and Research Center on Applied Mathematics
Masaru Sugiyama: Nagoya Institute of Technology

Chapter Chapter 33 in Classical and Relativistic Rational Extended Thermodynamics of Gases, 2021, pp 619-626 from Springer

Abstract: Abstract In this chapter, we discuss the parabolic limit of RET via the Maxwellian iteration, and we observe that the usual constitutive equations, which are nonlocal in space, are approximations of some balance laws of RET when some relaxation times are very small. 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 RET theories.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-59144-1_33

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DOI: 10.1007/978-3-030-59144-1_33

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