Uniqueness for structural phase transitions in shape memory alloys

摘要

AbstractThe non‐linear coupled equations arising from alloy mechanismdocumentclass{article}pagestyle{empty}begin{document}$$ begin{array}{*{20}c} {u_{tt} - aleft({u_x,theta } right)u_{xx} - mu u_{xxt} - bleft({u_x,theta } right)theta _x = fleft({x,t} right),} {cleft({u_x,theta } right)theta _t - ktheta _{xx} - alpha ktheta _{xxt} - mu u_{xt}^2 - dleft({u_x,theta } right)u_{xt} = lambda left({x,t} right),} end{array} $$end{document}have two important features: a may take negative values andcmay be degenerate.The local existence has been proved in Reference 1, but the uniqueness was open. In this paper the uniqueness is proved. For a discussion of the physical model and for the justifications of the detailed technical assumptions to be made, we refer to Reference