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| Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys | |
| 作者姓名： | Pierluigi COLLI Michel FREMOND Elisabetta ROCCA Ken SHIRAKAWA |
| 作者单位： | [1]Dipartimento di Matematica ＂F. Casorati＂, Universita degli Studi di Pavia, via Ferrata 1, 27100 Pavia, Ital [2]Laboratoire Central des Ponts et Chaussees, 58 Boulevard Lefebvre, 75732 Paris Cedex 15, France [3]Dipartimento di Matematica ＂F. Enriques＂, Universita degli Studi di Milano, via Saldini 50, 20133 Milano, Italy [4]Department of Applied Mathematics, Faculty of Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan |
| 基金项目： | Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”. |
| 摘 要： | |
| 关 键 词： | 外形记忆 热机模型 偏微分方程 整体吸引子 |
| 收稿时间： | 8 July 2005 |
Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys |
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| Pierluigi COLLI,Michel FREMOND,Elisabetta ROCCA,Ken SHIRAKAWA.Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys[J].Chinese Annals of Mathematics,Series B,2006,27(6):683-700. | |
| Authors: | Pierluigi COLLI Michel FREMOND Elisabetta ROCCA and Ken SHIRAKAWA |
| Affiliation: | 1. Dipartimento di Matematica "F. Casorati", Università degli Studi di Pavia, via Ferrata 1,27100 Pavia, Italy 2. Laboratoire Central des Ponts et Chaussées, 58 Boulevard Lefebvre, 75732 Paris Cedex 15, France 3. Dipartimento di Matematica "F. Enriques", Università degli Studi di Milano, via Saldini 50, 20133 Milano, Italy 4. Department of Applied Mathematics, Faculty of Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan |
| Abstract: | Abstract In this note, we consider a Frémond 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 12] 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. * Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”. |
| Keywords: | Shape memory Thermomechanical model Parabolic system of partial differential equations Global attractor |
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