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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.

Well-posedness of solutions to a phase-field model for the martensitic phase transformations