2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221749In this paper we study a model for phase segregation consisting in a sistem of a partial and an ordinary differential equation. By a careful definition of maximal solution to the latter equation, this system reduces to an Allen-Cahn equation with a memory term. Global existence and uniqueness of a smooth solution are proven and a characterization of the omega-limit set is given.Analysis of PDEs74A15, 35K55, 35A05, 35B40text