# Can constitutive relations be represented by non-local equations?

## Mercoledi' 1 giugno 2011 - Tommaso Ruggeri

ARGOMENTI: Seminari

SEMINARIO AMEC (congiunto di Analisi, MEccanica e Calcolo),
Mercoledi' 1 giugno 2011, Tommaso Ruggeri (Universita' di Bologna) terra' in Sala Riunioni VII dalle 11:00 alle 11:30 il prologo e in aula 1BC45 alle ore 12:15 il seminario dal titolo "Can constitutive relations be represented by non-local equations?".

-Abstract
The modern theory of extended thermodynamics shows that the popular "constitutive" equations of continuum mechanics of non-local form are in reality approximations of balance laws, when some relaxation times are neglected. We recall, for example, the Fourier's equation, the Navier-Stokes' equations, the Fick's equation, the Darcy's law and several others. This idea suggests that the "authentic" type of constitutive equations are local and, therefore, the differential systems of mathematical physics are hyperbolic rather than parabolic. Another consequence is that these equations do not need to satisfy the so called objectivity principle that on the contrary still continues to be valid only for the "authentic" constitutive equations. However these limit non-local equations are useful not only because they are used in normal physical situations but also because they permit to obtain the evaluation of non-observable quantities such as the velocity or the temperature of each constituent of a mixture. Considerations are also made with regard to the formal limits from parabolic versus hyperbolic and from hyperbolic versus hyperbolic, between a system and a subsystem. We discuss the main analytical properties with respect to the global existence of smooth solutions for dissipative hyperbolic systems.

Nel prologo di mezz'ora il conferenziere presentera' l'argomento del successivo seminario per permettere a tutti gli interessati una migliore comprensione del problema trattato.

Rif. int. M. Bardi, C. Marchi, F. Ancona