# American Institute of Mathematical Sciences

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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