Well-posedness and approximation for a one-dimensional model for shape memory alloys

This paper addresses a one-dimensional differential model describing the super-elastic effect in shape memory alloys. After a preliminary discussion on the model, we focus our attention on the study of the material constitutive relation and prove well-posedness and approximation results for some related initial value problem. Then, we turn our attention to the coupling of the constitutive law with a quasi-static momentum relation and solve the full PDE boundary value problem in one space dimension. In particular, we provide an existence and continuous dependence result and fully develop a spacetime discretization procedure.