We study a phase-field model, which describes the transformations for the austenite-martensite and the multiple twinning in Martensite. The model consists of two nonlinear parabolic equations of second order. We first show the existence of local solutions to an initial-boundary value problem by utilizing the Banach fixed-point theorem. Then we verify the solutions is global. Finally we investigate the regularity and uniqueness of the solution.

We show the existence of global-in-time solutions to an initial-boundary value problem in one space dimension of a phase-field model on the martensitic phase transformations, which consists of the equations of degenerate and a nondegenerate nonlinear parabolic equation of second order.