Phase Transitions and Generalized Motion by Mean Curvature
Phase Transitions and Generalized Motion by Mean Curvature
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DOI：
10.1002/cpa.3160450903
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发表时间：
1992-10
影响因子：
3
通讯作者：
L. Evans;H. Soner;P. Souganidis
中科院分区：
文献类型：
--
作者：
L. Evans;H. Soner;P. Souganidis
我们研究了艾伦-卡恩方程（动态相变的简化模型）的适当重新缩放版本的解的极限行为。我们严格地建立了一个相位反相界面的存在性，根据平均曲率运动的限制。这一论断对所有正时间都是有效的，即在几何奇点出现之后，在埃文斯-斯普拉克和陈-吉加-后藤的广义意义上解释的运动。
We study the limiting behavior of solutions to appropriately rescaled versions of the Allen-Cahn equation, a simplified model for dynamic phase transitions. We rigorously establish the existence in the limit of a phase-antiphase interface evolving according to mean curvature motion. This assertion is valid for all positive time, the motion interpreted in the generalized sense of Evans-Spruck and Chen-Giga-Goto after the onset of geometric singularities.