June  2007, 6(2): 367-387. doi: 10.3934/cpaa.2007.6.367

Global existence and long-time behaviour for a singular integro-differential phase-field system

1. 

Dipartimento di Matematica “F. Casorati”, Università degli Studi di Pavia, via Ferrata, 1, 27100, Pavia, Italy

2. 

Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, via Saldini, 50, 20133, Milano, Italy

Received  February 2006 Revised  August 2006 Published  March 2007

This paper deals with a singular integro-differential PDE system describing phase transitions in terms of nonlinear evolution equations for micromotions and for the entropy. The model is derived from a non-convex free energy functional, possibly accounting for thermal memory effects. After recovering a global existence result for a related initial and boundary value problem, the long-time behaviour of the solutions is investigated. In particular, it is proved that the elements of the $\omega$-limit set (i.e. the cluster points) of the solution trajectories solve the steady state system which is naturally associated to the evolution problem.
Citation: Elena Bonetti, Elisabetta Rocca. Global existence and long-time behaviour for a singular integro-differential phase-field system. Communications on Pure & Applied Analysis, 2007, 6 (2) : 367-387. doi: 10.3934/cpaa.2007.6.367
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