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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^{1}; Tesdall, Allen M.

^{2}

@article{CRMATH_2022__360_G1_35_0, author = {LeFloch, Philippe G. and Tesdall, Allen M.}, 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}, number = {G1}, year = {2022}, doi = {10.5802/crmath.278}, language = {en}, url = {http://www.numdam.org/articles/10.5802/crmath.278/} }

TY - JOUR AU - LeFloch, Philippe G. AU - Tesdall, Allen M. TI - The positive entropy production property for augmented nonlinear hyperbolic models JO - Comptes Rendus. Mathématique PY - 2022 SP - 35 EP - 46 VL - 360 IS - G1 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.278/ DO - 10.5802/crmath.278 LA - en ID - CRMATH_2022__360_G1_35_0 ER -

%0 Journal Article %A LeFloch, Philippe G. %A Tesdall, Allen M. %T The positive entropy production property for augmented nonlinear hyperbolic models %J Comptes Rendus. Mathématique %D 2022 %P 35-46 %V 360 %N G1 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.278/ %R 10.5802/crmath.278 %G en %F CRMATH_2022__360_G1_35_0

LeFloch, Philippe G.; Tesdall, Allen M. The positive entropy production property for augmented nonlinear hyperbolic models. Comptes Rendus. Mathématique, Volume 360 (2022) no. G1, pp. 35-46. doi : 10.5802/crmath.278. http://www.numdam.org/articles/10.5802/crmath.278/

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