On the existence of a weak solution to a free boundary problem for a model of a shape memory alloy spring

Toyohiko Aiki

doi:10.3934/dcdss.2012.5.1

Article Contents

2012, Volume 5, Issue 1: 1-13. Doi: 10.3934/dcdss.2012.5.1

This issue Previous Article Preface Next Article On a one-dimensional shape-memory alloy model in its fast-temperature-activation limit

On the existence of a weak solution to a free boundary problem for a model of a shape memory alloy spring

Toyohiko Aiki^1,

1.
Department of Mathematics, Faculty of Education, Gifu University, Yanagido 1-1, Gifu, 501-1193

Received: January 31, 2009

Revised: January 31, 2010

Published: January 2012

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Abstract

In our previous works we proposed and studied the mathematical model for the position of the joint of a shape memory alloy and a bias springs in case the temperature is known. The purpose of this paper is to establish a mathematical model with unknown temperature and to show a local existence of a solution to the model in time.

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Mathematics Subject Classification: Primary: 35R35.

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References

[1]	T. Aiki, A mathematical model for a valve made of a spring of a shape memory alloy, in "Nonlinear Phenomena with Energy Dissipation," GAKUTO International Series, Mathematical Sciences and Applications, 29 (2008), 1-18.
[2]	T. Aiki, The position of the joint of shape memory alloy and bias springs, submitted.
[3]	M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,'' Appl. Math. Sci., 121, Springer-Verlag, New York, 1996.