An exact macroscopic extended model with many moments

TL;DR

This paper develops an exact macroscopic extended thermodynamics model with many moments, providing a comprehensive framework that generalizes previous kinetic approaches and ensures hyperbolicity and finite wave speeds.

Contribution

It introduces a novel macroscopic approach for arbitrary moments in extended thermodynamics, extending and generalizing existing kinetic models.

Findings

The model guarantees hyperbolicity and finite wave speeds.

Constitutive functions are explicitly determined up to any order.

Kinetic approach results are recovered as a special case.

Abstract

Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of ordinary thermodynamics. Here its methods are applied to the case of an arbitrary, but fixed, number of moments. The kinetic approach has already been developed in literature; then, the macroscopic approach is here considered and the constitutive functions appearing in the balance equations are determined up to whatever order with respect to thermodynamical equilibrium. The results of the kinetic approach are a particular case of the present ones.