A nonlinear system for phase change with dissipation

Abstract

A nonlinear system modeling a phase change problem with dissipation is investigated. The model is derived with the thermodynamical theory of continuum mechanics; it includes among other features superheating and supercooling effects or irreversible phase changes. One of the equations is doubly nonlinear, with a nonlinearity on the time derivative of one of the unknowns and the resulting system is non-monotone in (L 2 ) 2 or in ( H-1 ) 2 . Uniqueness of the solution is proved using the accretivity of the system in ( L 1 ) 2 . The existence of a solution is shown through a regularization of one the nonlinearities. In this case, such a method permits to weaken the customary assumption of the L 1 -framework.