Given a first-order nonlinear hyperbolic system of conservation laws endowed with a convex entropy-entropy flux pair, we consider the class of weak solutions containing shock waves depending upon some small scale parameters. In this Note, after introducing a notion of positive entropy production property that involves test-functions (rather than solutions), we define and derive several classes of entropy-dissipating augmented models, as we call them, which involve (possibly nonlinear) second- and third-order augmentation terms. Such terms typically arise in continuum physics and model viscosity and other high-order effects in a fluid. By introducing a new notion of positive entropy production that concerns general functions rather than solutions, we can easily check the entropy-dissipating property for a broad class of augmented models. The weak solutions associated with the corresponding zero-limit may contain (nonclassical undercompressive) shocks whose selection is determined from these high-order effects, for instance by using traveling wave solutions. Having a classification of the underlying models, as we propose, is essential for developing a general shock wave theory.
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@article{CRMATH_2022__360_G1_35_0,
author = {Philippe G. LeFloch and Allen M. Tesdall},
title = {The positive entropy production property for augmented nonlinear hyperbolic models},
journal = {Comptes Rendus. Math\'ematique},
pages = {35--46},
publisher = {Acad\'emie des sciences, Paris},
volume = {360},
year = {2022},
doi = {10.5802/crmath.278},
language = {en},
}
TY - JOUR AU - Philippe G. LeFloch AU - Allen M. Tesdall TI - The positive entropy production property for augmented nonlinear hyperbolic models JO - Comptes Rendus. Mathématique PY - 2022 SP - 35 EP - 46 VL - 360 PB - Académie des sciences, Paris DO - 10.5802/crmath.278 LA - en ID - CRMATH_2022__360_G1_35_0 ER -
Philippe G. LeFloch; Allen M. Tesdall. The positive entropy production property for augmented nonlinear hyperbolic models. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 35-46. doi : 10.5802/crmath.278. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.278/
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