# American Institute of Mathematical Sciences

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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