Uniqueness for structural phase transitions in shape memory alloys

The non‐linear coupled equations arising from alloy mechanism\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {u_{tt} - a\left({u_x,\theta } \right)u_{xx} - \mu u_{xxt} - b\left({u_x,\theta } \right)\theta _x = f\left({x,t} \right),} \\ {c\left({u_x,\theta } \right)\theta _t - k\theta _{xx} - \alpha k\theta _{xxt} - \mu u_{xt}^2 - d\left({u_x,\theta } \right)u_{xt} = \lambda \left({x,t} \right),} \\\end{array} $$\end{document}have two important features: a may take negative values and c may 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 1.