Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys

在这笔记，我们考虑形状记忆合金的一个 Fremond 模型。让我们想象在它的边界的一部分上被修理的一一形状记忆合金，并且假定那强迫条款，例如，留下上的热来源和外部应力它的边界分开，收敛到一些时间无关的功能在适当意义，作为时间去无穷。Underthe 上面的假设，我们将从全球引起注意的人的观点为动态系统讨论 asymptotic 稳定性。更精确，我们概括纸[12 ] 处理 theone 维的大小写。首先，我们为限制显示出全球引起注意的人的存在自治动态系统；然后，我们由限制为 non-autonomouscase 描绘 asymptotic 稳定性全球引起注意的人。

In this note, we consider a Fremond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, 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 generalize the paper dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor.