A well-posedness result for irreversible phase transitions with a nonlinear heat flux law
Giovanna Bonfanti Fabio Luterotti
Discrete & Continuous Dynamical Systems - S 2013, 6(2): 331-351 doi: 10.3934/dcdss.2013.6.331
In this paper, we deal with a PDE system describing a phase transition problem characterized by irreversible evolution and ruled by a nonlinear heat flux law. Its derivation comes from the modelling approach proposed by M. Frémond. Our main result consists in showing the global-in-time existence and the uniqueness of the solution of the related initial and boundary value problem.
keywords: existence Phase changes uniqueness. irreversibility microscopic movements
Global solution to a phase transition model with microscopic movements and accelerations in one space dimension
Giovanna Bonfanti Fabio Luterotti
Communications on Pure & Applied Analysis 2006, 5(4): 763-777 doi: 10.3934/cpaa.2006.5.763
This note deals with a nonlinear system of PDEs accounting for phase transition phenomena. The existence of solutions of a related Cauchy-Neumann problem is established in the one-dimensional setting. A fixed point procedure guarantees the existence of solutions locally in time. Next, an argument based on a priori estimates allows to extend such solutions in the whole time interval. Hence, the uniqueness of the solution is proved by proper contracting estimates.
keywords: Phase transitions existence and uniqueness results. microscopic movements

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