We investigate a partial differential equation which models solid‐solid phase transitions. This model is for martensitic phase transitions driven by configurational force and its counterpart is for interface motion by mean curvature. Mathematically, this equation is a second‐order nonlinear degenerate parabolic equation. And in multidimensional case, its principal part cannot be written into divergence form . We prove the existence and uniqueness of viscosity solution to a Cauchy problem for this model.

中文翻译：

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固-固相变的相场模型柯西问题的粘度解

我们研究了偏微分方程，该方程对固-固相变建模。该模型用于由构型力驱动的马氏体相变，而其对应模型用于通过平均曲率进行界面运动。在数学上，该方程是二阶非线性简并抛物线方程。而且在多维情况下，其主要部分不能写为发散形式。我们证明了该模型对柯西问题的粘性解的存在性和唯一性。