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Extended thermodynamics—a theory of symmetric hyperbolic field equations

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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.

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  1. Technische Universität Berlin, Straße des 17. Juni 135, 10623, Berlin, Germany

    Ingo Müller

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  1. Ingo Müller
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Correspondence to Ingo Müller.

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Dedicated to Jürgen Sprekels on the occasion of his 60th birthday

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Müller, I. Extended thermodynamics—a theory of symmetric hyperbolic field equations. Appl Math 53, 469–484 (2008). https://doi.org/10.1007/s10492-008-0037-6

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