Boundary blow-up solutions with interior layers and spikes in a bistable problem

Yihong Du; Zongming Guo; Feng Zhou

doi:10.3934/dcds.2007.19.271

Boundary blow-up solutions with interior layers and spikes in a bistable problem

Yihong Du, Zongming Guo, Feng Zhou

School of Mathematical Sciences

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

19 Scopus citations

Abstract

We show that for small ε > 0, the boundary blow-up problem -ε²Δu = u(u - a(x))(1 - u) in Ω, u|∂Ω = ∞ has solutions with sharp interior layers and spikes, apart from boundary layers. We also determine the location of these layers and spikes.

Original language	English
Pages (from-to)	271-298
Number of pages	28
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	19
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2007.19.271
State	Published - Oct 2007

Keywords

Bistable
Boundary and interior layer
Boundary blow-up
Reduction method
Spike layer

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10.3934/dcds.2007.19.271

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title = "Boundary blow-up solutions with interior layers and spikes in a bistable problem",

abstract = "We show that for small ε > 0, the boundary blow-up problem -ε2Δu = u(u - a(x))(1 - u) in Ω, u|∂Ω = ∞ has solutions with sharp interior layers and spikes, apart from boundary layers. We also determine the location of these layers and spikes.",

keywords = "Bistable, Boundary and interior layer, Boundary blow-up, Reduction method, Spike layer",

author = "Yihong Du and Zongming Guo and Feng Zhou",

year = "2007",

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AU - Du, Yihong

AU - Guo, Zongming

AU - Zhou, Feng

PY - 2007/10

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N2 - We show that for small ε > 0, the boundary blow-up problem -ε2Δu = u(u - a(x))(1 - u) in Ω, u|∂Ω = ∞ has solutions with sharp interior layers and spikes, apart from boundary layers. We also determine the location of these layers and spikes.

AB - We show that for small ε > 0, the boundary blow-up problem -ε2Δu = u(u - a(x))(1 - u) in Ω, u|∂Ω = ∞ has solutions with sharp interior layers and spikes, apart from boundary layers. We also determine the location of these layers and spikes.

KW - Bistable

KW - Boundary and interior layer

KW - Boundary blow-up

KW - Reduction method

KW - Spike layer

UR - https://www.scopus.com/pages/publications/36049037317

U2 - 10.3934/dcds.2007.19.271

DO - 10.3934/dcds.2007.19.271

M3 - 文章

AN - SCOPUS:36049037317

SN - 1078-0947

VL - 19

SP - 271

EP - 298

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 2

ER -

Boundary blow-up solutions with interior layers and spikes in a bistable problem

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Keywords

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