Geodesic
The entropy principle: from continuum mechanics to hyperbolic systems of balance laws
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 1, pp. 1-20.

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We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for smooth solutions. At the end we give some recent results on closure procedure for the moments theory associated to the Boltzmann equation (Extended Thermodynamics).
Si presenta una breve rassegna dei diversi ruoli che ha il principio di entropia nella moderna termodinamica. Nell'ambito della termodinamica razionale il principio di entropia diventa un criterio di selezione per le equazioni costitutive ammissibili mentre nel caso di soluzioni deboli di sistemi iperbolici non lineari diventa un criterio di selezione dei processi fisicamente ammissibili. Inoltre tutti i sistemi iperbolici di leggi di bilancio che sono compatibili con un principio di entropia convessa sono simmetrici ed è possibile riconoscere teorie a nido mediante l'introduzione dei sottosistemi principali. Particolare attenzione è dedicata all’analisi qualitativa dimostrando che in presenza di dissipazione il problema di Cauchy è ben posto in senso globale ed esistono, per dati iniziali sufficientemente piccoli, soluzioni regolari per tutti i tempi che tendono a stati costanti di equilibrio. Infine vengono applicati questi risultati alla teoria della Termodinamica Estesa che governa i processi dei gas rarefatti. 
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Ruggeri, Tommaso. The entropy principle: from continuum mechanics to hyperbolic systems of balance laws. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 1, pp. 1-20. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_1_a0/

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