位形力驱动下固体相变模型的行波解
Traveling waves for models of phase transitions of solids driven by configurational forces
摘要：
本文讨论了几种基于构形力的模型的行波解（包括驻波）的存在性，分别描述了固体材料的无扩散相变，例如，钢，以及由于界面扩散引起的界面运动引起的相变，例如，在烧结法这些模型是最近由Alber和Zhu提出的。在适当的假设下，我们考虑了序参数守恒和非守恒的情形。此外，我们比较我们的结果与相应的Allen-Cahn和Cahn-Hilliard方程耦合线性弹性，这是模型的扩散为主的相变在弹性固体。
英文摘要：
This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transformations of solid materials, e.g., Steel, and phase transitions due to interface motion by interface diffusion, e.g., Sintering. These models are recently proposed by Alber and Zhu. We consider both the order-parameter-conserved case and the non-conserved one, under suitable assumptions. Also we compare our results with the corresponding ones for the Allen-Cahn and the Cahn-Hilliard equations coupled with linear elasticity, which are models for diffusion-dominated phase transformations in elastic solids.
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