Viscosity solutions to a model for solid-solid phase transitions driven by material forces

A new phase-field model is formulated to describe martensitic phase transitions driven by material forces, in solid materials, e.g., shape memory alloys. This model is a nonlinear degenerate parabolic equation of second order and its principal part is not in divergence form in multi-dimensional case. The global existence of viscosity solutions to an initial-boundary value problem for this model is proved.