Ruggeri, Tommaso:
The entropy principle: from continuum mechanics to hyperbolic systems of balance laws
Bollettino dell'Unione Matematica Italiana Serie 8 8-B (2005), fasc. n.1, p. 1-20, Unione Matematica Italiana (English)
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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 allanalisi 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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