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.

中文翻译：

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马氏体相变相场模型解的适定性

我们研究了一个相场模型，该模型描述了奥氏体-马氏体的转变和马氏体中的多重孪晶。该模型由两个二阶非线性抛物方程组成。我们首先利用 Banach 不动点定理证明了初始边值问题的局部解的存在。然后我们验证解决方案是全球性的。最后我们研究解的规律性和唯一性。