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A note on interface formation in singularly perturbed elliptic problems
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2020-10-06 , DOI: 10.1080/17476933.2020.1825395 M. Sônego 1
中文翻译:
奇异摄动椭圆问题中界面形成的注解
更新日期:2020-10-06
Complex Variables and Elliptic Equations ( IF 0.9 ) Pub Date : 2020-10-06 , DOI: 10.1080/17476933.2020.1825395 M. Sônego 1
Affiliation
In this note, we prove that the equal-area condition is necessary for the formation of internal transition layer by the solutions of a general singularly perturbed elliptic problem. Our result is independent of boundary conditions, it improves previous references in the literature and can be applied to Allen-Cahn, Sine-Gordon and Fisher-KPP equations, for example.
中文翻译:
奇异摄动椭圆问题中界面形成的注解
在这篇笔记中,我们通过一般奇异摄动椭圆问题的解证明了等面积条件对于内部过渡层的形成是必要的。我们的结果与边界条件无关,它改进了文献中的参考文献,例如可以应用于 Allen-Cahn、Sine-Gordon 和 Fisher-KPP 方程。