Generators of hyperbolic heat equation in nonlinear thermoelasticity

Tommaso Ruggeri

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Displaying similar documents to “Generators of hyperbolic heat equation in nonlinear thermoelasticity”

On a supplementary conservation law for a hyperbolic model of heat conductor

Mariano Torrisi, Antonino Valenti (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In the context of the wave propagation theory in nonlinear hyperbolic systems, we analyse, in the case of a rigid heat conductor, the model proposed by G. Grioli. After introducing the constitutive relations according to the point of view of the extended thermodynamics, we look for the compatibility of the governing equations with a supplementary conservation law. We obtain the functional form of the constitutive quantities and we are able to show that the governing equations may be...

Entropy flux far from equilibrium in solids and in non viscous gases

M. S. Mongiovì, R. A. Peruzza (2004)

Bollettino dell'Unione Matematica Italiana

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One of the main question arising in Extended Thermodynamics concerns the physical meaning of the temperature far from equilibrium. Some authors define thermodynamic temperature $T_{t h}$ the inverse of the coefficient linking the entropy flux with the heat flux. Other authors, instead, define non-equilibrium temperature $θ$ the inverse of the partial derivative of entropy with respect to energy, at density and heat flux constant. The aim of this paper is to determine the expression of entropy...

On a covariant formulation of dissipative phenomena

D. Pavón, D. Jou, J. Casas-Vázquez (1982)

Annales de l'I.H.P. Physique théorique

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The Hamilton Principle for Fluid Binary Mixtures with two Temperatures

Henri Gouin, Tommaso Ruggeri (2009)

Bollettino dell'Unione Matematica Italiana

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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...

Supplementary balance laws for Cattaneo heat propagation

Serge Preston (2013)

Communications in Mathematics

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In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (shortly SBL) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature ( $λ^{0} (ϑ), K^{A} (ϑ), A = 1, 2, 3$ ). The requirements of the II law...

The entropy principle: from continuum mechanics to hyperbolic systems of balance laws

Tommaso Ruggeri (2005)

Bollettino dell'Unione Matematica Italiana

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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...