IJPAM: Volume 52, No. 1 (2009)

A POSSIBLE SOLUTION FOR AN OPEN PROBLEM
IN EXTENDED THERMODYNAMICS

M.C. Carrisi$^1$, S. Pennisi$^2$, A.R. Pillosu$^3$
$^{1,2,3}$Dipartimento di Matematica ed Informatica
Universitá di Cagliari
Via Ospedale 72, Cagliari, 09124, ITALY
$^1$e-mail: cristina.carrisi@tiscali.it
$^2$e-mail: spennisi@unica.it
$^3$e-mail: anri.p78@virgilio.it


Abstract.Some years ago, Professor Brini and Ruggeri exploited the $ET^{\alpha}_{m}$ theories, that is theories in Extended Thermodynamics of $m$ moments and of degree $\alpha$; the index $\alpha$ represents the approximation degree for the distribution function, through its formal expansion in the neighborhood of the Maxwellian distribution. They proved, through simple examples of stationary problems that the entropy principle fails in general, if all the non-equilibrium variables are of the same order of magnitude; this is because some ``critical derivatives" are not small along all the solutions.

Here we show that the above results do not mean that in the previous theory there is something wrong. We show also other ways to overcome the above mentioned difficulties.

Received: March 20, 2009

AMS Subject Classification: 80A10

Key Words and Phrases: extended thermodynamics, entropy principle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 1