Irreversible Phase Changes

Abstract

This paper deals with mathematical results concerning systems modelling some dissipative phase changes phenomena. These models can be derived through the usual thermodynamical theory of continuous mechanics (see [2], [5]). The systems under investigation are of the form.

$$c\left( x \right)\frac{{d\theta }}{{dt}} + \frac{{d\chi }}{{dt}} - div\kappa \left( x \right)\nabla \theta = 0in\Omega \times \left( {0,T,} \right)$$

(1.1)

$$\frac{{d\chi }}{{dt}} + \partial \emptyset \left( {x,\frac{{d\chi }}{{dt}}} \right) + \partial \psi \left( {x,\chi } \right) \mathrel\backepsilon \theta in\Omega \times \left( {0,T} \right)$$

(1.2)

$$\theta = 0in\partial \Omega \times \left( {0,T} \right)$$

(1.3)

$$\theta \left( {t = 0} \right) = \theta o,\chi \left( {t = 0} \right) = \chi oin\Omega$$

(1.4)