论文标题
边界条件对二阶奇异扰动相变模型对$ \ mathbb {r} $的影响
Effect of Boundary Conditions on Second-Order Singularly-Perturbed Phase Transition Models on $\mathbb{R}$
论文作者
论文摘要
二阶单位扰动问题涉及积分功能$ \int_Ω\ varepsilon_n^{ - 1} $ \ varepsilon_n \ to 0^+$的正元素和一个函数$ w：\ mathbb {r} \ to [0，\ infty）$，完全有两个不同的零。该功能引起了人们的关注，因为它将相转换的行为建模，并且Fonseca和Mantegazza研究了其伽玛限制为$ n \ to \ infty $。在本文中，我们研究了$ n = 1 $的问题的实例。我们找到了伽马极限的不同形式，并在添加边界数据下研究了伽马极限。
The second-order singularly-perturbed problem concerns the integral functional $\int_Ω\varepsilon_n^{-1}W(u) + \varepsilon_n^3\|\nabla^2u\|^2\,dx$ for a bounded open set $Ω\subseteq \mathbb{R}^N$, a sequence $\varepsilon_n \to 0^+$ of positive reals, and a function $W:\mathbb{R} \to [0,\infty)$ with exactly two distinct zeroes. This functional is of interest since it models the behavior of phase transitions, and its Gamma limit as $n \to \infty$ was studied by Fonseca and Mantegazza. In this paper, we study an instance of the problem for $N=1$. We find a different form for the Gamma limit, and study the Gamma limit under the addition of boundary data.
