December  2006, 5(4): 763-777. doi: 10.3934/cpaa.2006.5.763

Global solution to a phase transition model with microscopic movements and accelerations in one space dimension

1. 

Dipartimento di Matematica, Università di Brescia, via Branze 38, 25123 Brescia, Italy, Italy

Received  December 2005 Revised  April 2006 Published  September 2006

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.
Citation: Giovanna Bonfanti, Fabio Luterotti. Global solution to a phase transition model with microscopic movements and accelerations in one space dimension. Communications on Pure & Applied Analysis, 2006, 5 (4) : 763-777. doi: 10.3934/cpaa.2006.5.763
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