On the dissipativity of a hyperbolic phase-field system with memory

A phase-field system with memory characterized by a heat conduction law of Gurtin-Pipkin type is considered, This model has been already studied by se veral authors who have obtained various well-posedness results. The longter m behavior of a single solution has also been investigated. In this note we first formulate the model as a dynamical system in a suitable phase space which accounts for the whole past history of the temperature. Then we prove the existence of a (uniform) absorbing set which basically shows the dissi pative nature of the system. Existence of a compact attractor is discussed as well.