Layer solutions for a one-dimensional nonlocal model of Ginzburg–Landau type
Layer solutions for a one-dimensional nonlocal model of Ginzburg–Landau type
复制标题
Ginzburg-Landau 型一维非局部模型的层解
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
X. Yan
中科院分区：
文献类型：
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作者：
K.;C. Muratov;X. Yan
我们研究了一个Ginzburg-Landau型的非局部模型，它产生了一个包含Laplacian和半Laplacian的混合方程。我们的重点是一维过渡层的配置文件，连接两个不同的均相。我们首先引入一个重正化的一维能量，是免费的对数发散由于失败的Gagliardo范数是有限的光滑的配置文件，渐近到不同的限制在无穷远。然后，我们证明了存在性，唯一性，单调性和正则性的极小在一个合适的类。最后，我们考虑了拉普拉斯算子前的系数为零的奇异极限，并证明了所得到的极小解收敛于分数阶Allen-Cahn方程的解。
We study a nonlocal model of Ginzburg–Landau type that gives rise to an equation involving a mixture of the Laplacian and half-Laplacian. Our focus is on one-dimensional transition layer profiles that connect the two distinct homogeneous phases. We first introduce a renormalized one-dimensional energy that is free from a logarithmic divergence due to the failure of the Gagliardo norm to be finite on smooth profiles that asymptote to different limits at infinity. We then prove existence, uniqueness, monotonicity and regularity of minimizers in a suitable class. Lastly, we consider the singular limit in which the coefficient in front of the Laplacian vanishes and prove convergence of the obtained minimizer to the solutions of the fractional Allen–Cahn equation.
影响因子：
1.7
作者：
Raetz, Andreas;Roeger, Matthias
通讯作者：
Roeger, Matthias