Connectivity of boundaries by clustering phase transition layers of Fife-Greenlee problem on smooth bounded domain

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Wei, Suting^1,2  Yang, Jun^2,3 

[1] South China Agr Univ, Dept Math, Guangzhou 510642, Peoples R China

[2] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[3] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China

关键词: Fife-Greenlee problem;    Multiple phase transition layers;    Resonance;    Toda system;   

DOI  :  10.1016/j.jde.2020.01.014

来源: Elsevier

【 摘 要 】

We consider the Fife-Greenlee problem epsilon(2)Delta u + (u - a(y)) (1-u(2)) = 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Omega is a bounded domain in R-2 with smooth boundary, epsilon > 0 is a small parameter, nu denotes the unit outward normal of partial derivative Omega. Let Gamma ={y epsilon Omega : a(y) = 0} be a simple smooth curve intersecting orthogonally with partial derivative Omega at exactly two points and dividing Omega into two disjoint nonempty components. We assume that -1 < a(y) < 1 on Omega and del a not equal 0 on Gamma, and also some admissibility conditions hold for a, Gamma and partial derivative Omega. For any fixed integer N = 2m + 1 >= 3, we will show the existence of a clustered solution uewith N-transition layers near Gamma with mutual distance O(epsilon vertical bar log epsilon vertical bar), provided that estays away from a discrete set of values at which resonance occurs. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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