# American Institute of Mathematical Sciences

February  2012, 5(1): 1-13. doi: 10.3934/dcdss.2012.5.1

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

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

Received  February 2009 Revised  February 2010 Published  February 2011

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.
Citation: Toyohiko Aiki. On the existence of a weak solution to a free boundary problem for a model of a shape memory alloy spring. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 1-13. doi: 10.3934/dcdss.2012.5.1
##### References:
 [1] T. Aiki, A mathematical model for a valve made of a spring of a shape memory alloy,, in, 29 (2008), 1.   Google Scholar [2] T. Aiki, The position of the joint of shape memory alloy and bias springs,, submitted., ().   Google Scholar [3] M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,'', Appl. Math. Sci., (1996).   Google Scholar

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##### References:
 [1] T. Aiki, A mathematical model for a valve made of a spring of a shape memory alloy,, in, 29 (2008), 1.   Google Scholar [2] T. Aiki, The position of the joint of shape memory alloy and bias springs,, submitted., ().   Google Scholar [3] M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,'', Appl. Math. Sci., (1996).   Google Scholar
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