Analysis of a solid-solid phase transition model coupling hyperbolic momentum balance and diffusive phase dynamics

This work deals with a nonlinear system modelling solid-solid phase transitions and mechanical deformations in shape memory alloys. The model is studied in the non-stationary case and accounts for local microscopic interactions between the different phases introducing the gradients of the phase parameters as state variables. By using an approximation—a priori estimates—passage to the limit procedure we prove the existence and uniqueness of a weak solution to the corresponding initial-boundary value problem and give some regularity results. Moreover, continuous dependence on the data of solutions is proved under stronger regularity assumptions on the data.