Generators of hyperbolic heat equation in nonlinear thermoelasticity
The entropy principle: from continuum mechanics to hyperbolic systems of balance laws
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....
A static coordinates and inequalities in Cosserat's continuum
Usando una naturale estensione delle coordinate astatiche ed iperastatiche della teoria classica dei continui si stabiliscono delle corrispondenti proprietà di media per lo stato tensionale nel caso dei continui di Cosserat. La presenza della parte emisimmetrica dello stress restringe le quantità dei valori medi di prodotti dello stress per coordinate che nel caso classico era possibile esprimere in funzione della sollecitazione esterna. Inoltre, non permette di determinare i valori medi delle coppie...
Su una naturale estensione a tre variabili dell'equazione di Monge-Ampère
It will be shown that the condition of exceptionality for all the discontinuity-waves of the equation , , reduces this to a straightforward generalization of the Monge-Ampère equation in three variables.
Su alcune classi di potenziali termodinamici come conseguenza dell'esistenza di particolari onde di discontinuità nella meccanica dei continui con deformazioni finite
Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics
The Hamilton Principle for Fluid Binary Mixtures with two Temperatures
For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the total heat exchange between components. In this nonconservative case, a Gibbs dynamical identity connecting the equations of momenta, masses, energy and heat exchange allows to deduce the balance equation of energy of the mixture. Due to the unknown exchange of...
Hamiltonian principle in the binary mixtures of Euler fluids with applications to the second sound phenomena
In the present paper we compare the theory of mixtures based on Rational Thermomechanics with the one obtained by Hamilton principle. We prove that the two theories coincide in the adiabatic case when the action is constructed with the intrinsic Lagrangian. In the complete thermodynamical case we show that we have also coincidence in the case of low temperature when the second sound phenomena arises for superfluid Helium and crystals.
Onde di discontinuità e condizioni dì eccezionalità per materiali ferromagnetici
We studied the propagation of first-order electromagnetic discontinuities through ferromagnetic materials whose magnetic permeability is a function of . We examined the condition for a discontinuity-wave not to generate a shock-wave (exceptionality conditions of Lax—Boillat). We found that the system is never fully exceptional, unless inthe plane wave case, if one supposes , or for with materials whose magnetic permeability solves a suitable differential equation.
Soluzioni lineari per la propagazione del calore in fluidodinamica relativistica
We look for simple waves and for solutions with separate variables of the linearized equations for heat propagation with finite velocities. We compare the results with the classical ones.
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