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The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo-Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo-Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier's law does not. [ABSTRACT FROM AUTHOR]

This paper deals with the long-term properties of the thermoelastic nonlinear string-beam system related to the well-known Lazer-McKenna suspension bridge model [ABSTRACT FROM AUTHOR]

A unified phase-field continuum theory is developed for transition and separation phenomena. A nonlocal formulation of the second law which involves an extra-entropy flux gives the basis of the thermodynamic approach. The phase-field is regarded as an additional variable related to some phase concentration, and its evolution is ruled by a balance equation, where flux and source terms are (unknown) constitutive functions. This evolution equation reduces to an equation of the rate-type when the flux is negligible, and it takes the form of a diffusion equation when the source term is disregarded. On this background, a general model for first-order transition and separation processes in a compressible fluid or fluid mixture is developed. Upon some simplifications, we apply it to the liquid-vapor phase change induced either by temperature or by pressure and we derive the expression of the vapor pressure curve. Taking into account the flux term, the sign of the diffusivity is discusssed. [ABSTRACT FROM AUTHOR]

In this paper we investigate mathematical models describing deformations and thermal variations of a thin homogeneous thermoviscoelastic plate. A hereditary non-Fourier constitutive law for the heat flux and some heat power constitutive equation with linear memory are considered. The resulting models are derived in the framework of the well-established theory, due to Gurtin and Pipkin, and according to the standard approximation procedure for the Reissner–Mindlin plate model. [ABSTRACT FROM AUTHOR]

In this paper we investigate mathematical models of a thin homogeneous thermoviscoelastic plate subject to thermal deformations. A non-Fourier constitutive law for the heat flux and some heat power constitutive equation with linear memory are considered here. The resulting models are derived in the framework of the well-established theory of heat flow with memory due to Gurtin and Pipkin and according to the standard approximation procedure for the Kirchhoff plate. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue including scientist Mauro Fabrizio, mathematical models and thermodynamics.