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| Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys |
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Citation： |
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 B,2006,27(6):683~700 |
| Page view： 1250
Net amount： 1002 |
Authors： |
Pierluigi COLLI; Michel FREMOND;Elisabetta ROCCA;Ken SHIRAKAWA |
Foundation： |
Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis
of Free Boundary Problems”. |
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| Abstract： |
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 [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. |
Keywords： |
Shape memory, Thermomechanical model, Parabolic system of partial
differential equations, Global attractor |
Classification： |
35K55, 35B41, 74D10 |
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