Time-periodic boundary layer solutions to singularly perturbed parabolic problems

被引：19

作者：

Omel'chenko, O. E. ^{[1
]}

Recke, L. ^{[2
]}

Butuzov, V. F. ^{[3
]}

Nefedov, N. N. ^{[3
]}

机构：

[1] Weierstrass Inst Appl Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany

[2] Humboldt Univ, Inst Math, Rudower Chausse 25, D-12489 Berlin, Germany

[3] Moscow MV Lomonosov State Univ, Fac Phys, Dept Math, Moscow 19899, Russia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 09期

关键词：

Monotone and non-monotone boundary layers; Two independent singular perturbation parameters; Periodic-parabolic boundary value problem; Implicit function theorem; EXISTENCE; STABILITY;

D O I：

10.1016/j.jde.2016.12.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we present a result of implicit function theorem type, which was designed for applications to singularly perturbed problems. This result is based on fixed point iterations for contractive mappings, in particular, no monotonicity or sign preservation properties are needed. Then we apply our abstract result to time-periodic boundary layer solutions (which are allowed to be non-monotone with respect to the space variable) in semilinear parabolic problems with two independent singular perturbation parameters. We prove existence and local uniqueness of those solutions, and estimate their distance to certain approximate solutions. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：4823 / 4862

页数：40

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