论文标题
脉动直立波和爱因斯坦关系的变分原理在尖锐的界面极限下
A Variational Principle for Pulsating Standing Waves and an Einstein Relation in the Sharp Interface Limit
论文作者
论文摘要
本文研究了周期性媒体中艾伦 - 卡恩能量功能的有效大规模行为与相关$ l^{2} $梯度流的尖锐接口限制之间的联系。通过在气缸$ \ mathbb {r} \ times \ mathbb {t}^{d} $中引入percival-type lagrangian，我们在$γ$ -Convergence的结果之间建立了一个链接。在层流介质中，我们在图形环境中证明了尖锐的界面限制，除了足够的系数平滑度之外，没有其他假设，并且证明有效的界面速度和表面张力可以满足爱因斯坦的关系。提出了许多病理，以突出在空间均匀环境中不会出现的困难。
This paper investigates the connection between the effective, large scale behavior of Allen-Cahn energy functionals in periodic media and the sharp interface limit of the associated $L^{2}$ gradient flows. By introducing a Percival-type Lagrangian in the cylinder $\mathbb{R} \times \mathbb{T}^{d}$, we establish a link between the $Γ$-convergence results of Anisini, Braides, and Chiadò Piat and the sharp interface limit results of Barles and Souganidis. In laminar media, we prove a sharp interface limit in a graphical setting, making no assumptions other than sufficient smoothness of the coefficients, and we prove that the effective interface velocity and surface tension satisfy an Einstein relation. A number of pathologies are presented to highlight difficulties that do not arise in the spatially homogeneous setting.
