Extended thermodynamics---a theory of symmetric hyperbolic field equations

Ingo Müller

Applications of Mathematics (2008)

  • Volume: 53, Issue: 5, page 469-484
  • ISSN: 0862-7940

Abstract

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Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear differential equations of first order. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation, provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation.

How to cite

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Müller, Ingo. "Extended thermodynamics---a theory of symmetric hyperbolic field equations." Applications of Mathematics 53.5 (2008): 469-484. <http://eudml.org/doc/37796>.

@article{Müller2008,
abstract = {Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear differential equations of first order. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation, provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation.},
author = {Müller, Ingo},
journal = {Applications of Mathematics},
keywords = {thermodynamics; symmetric hyperbolicity; kinetic theory; light scattering; thermodynamics; symmetric hyperbolicity; kinetic theory; light scattering},
language = {eng},
number = {5},
pages = {469-484},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extended thermodynamics---a theory of symmetric hyperbolic field equations},
url = {http://eudml.org/doc/37796},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Müller, Ingo
TI - Extended thermodynamics---a theory of symmetric hyperbolic field equations
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 5
SP - 469
EP - 484
AB - Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear differential equations of first order. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation, provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation.
LA - eng
KW - thermodynamics; symmetric hyperbolicity; kinetic theory; light scattering; thermodynamics; symmetric hyperbolicity; kinetic theory; light scattering
UR - http://eudml.org/doc/37796
ER -

References

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