Evolution of phase boundaries by configurational forces

An initial boundary value problem modeling the evolution of phase interfaces in materials showing martensitic transformations is studied. The model, which is derived rigorously from a sharp interface model with phase interfaces driven by configurational forces and which generalizes that model, consists of the equations of linear elasticity coupled with a nonlinear partial differential equation of hyperbolic character governing the evolution of the order parameter. It is proved that in one space dimension, global solutions exist for which the order parameter belongs to the space of functions of bounded variation. Other models for interface motion by martensitic transformations and by interface diffusion are suggested.