Boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions

Yihong Du; Zongming Guo

doi:10.1016/j.jde.2005.08.006

Boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions

Yihong Du
, Zongming Guo

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We show that for large λ>0, the 'generalized' boundary value problem −Δu = λu(u − a(x))(1 − u) in Ω, u|∂Ω = ø, where 1≼ø(x)≼∞, behaves like the special case ø ≡ 1. In particular, we show the existence of solutions with sharp boundary layers and interior spikes, and determine the location of the spikes.

Original language	English
Pages (from-to)	102-133
Journal	Journal of Differential Equations
Volume	221
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2005.08.006
Publication status	Published - 2006

Keywords

Ordinary Differential Equations, Difference Equations and Dynamical Systems

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10.1016/j.jde.2005.08.006

https://hdl.handle.net/1959.11/3850

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title = "Boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions",

abstract = "We show that for large λ>0, the 'generalized' boundary value problem −Δu = λu(u − a(x))(1 − u) in Ω, u|∂Ω = {\o}, where 1≼{\o}(x)≼∞, behaves like the special case {\o} ≡ 1. In particular, we show the existence of solutions with sharp boundary layers and interior spikes, and determine the location of the spikes.",

keywords = "Ordinary Differential Equations, Difference Equations and Dynamical Systems",

author = "Yihong Du and Zongming Guo",

year = "2006",

doi = "10.1016/j.jde.2005.08.006",

language = "English",

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pages = "102--133",

journal = "Journal of Differential Equations",

issn = "0022-0396",

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T1 - Boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions

AU - Du, Yihong

AU - Guo, Zongming

PY - 2006

Y1 - 2006

N2 - We show that for large λ>0, the 'generalized' boundary value problem −Δu = λu(u − a(x))(1 − u) in Ω, u|∂Ω = ø, where 1≼ø(x)≼∞, behaves like the special case ø ≡ 1. In particular, we show the existence of solutions with sharp boundary layers and interior spikes, and determine the location of the spikes.

AB - We show that for large λ>0, the 'generalized' boundary value problem −Δu = λu(u − a(x))(1 − u) in Ω, u|∂Ω = ø, where 1≼ø(x)≼∞, behaves like the special case ø ≡ 1. In particular, we show the existence of solutions with sharp boundary layers and interior spikes, and determine the location of the spikes.

KW - Ordinary Differential Equations, Difference Equations and Dynamical Systems

U2 - 10.1016/j.jde.2005.08.006

DO - 10.1016/j.jde.2005.08.006

M3 - Article

SN - 0022-0396

VL - 221

SP - 102

EP - 133

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions

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