Attractors for the one-dimensional Frémond model of shape memory alloys

In this paper, we consider a one-dimensional Frémond model of shape memory alloys. Let us imagine a wire of a shape memory alloy whose left hand side is fixed, and assume that forcing terms, e.g., heat sources and external stress on the right hand side, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we first show the existence of the global attractor for the limiting autonomous dynamical system, for instance the case of zero external stress, and secondly, characterize the asymptotic stability for non-autonomous case by the limiting global attractor.