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

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2007, 19(2): 271-298. doi: 10.3934/dcds.2007.19.271

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

Yihong Du ^1, , Zongming Guo ^2, and Feng Zhou ^3,

1.	School of Mathematics, Statistics and Computer Science, University of New England, Armidale, NSW 2351
2.	Department of Mathematics, Henan Normal University, Xinxiang, 453007, China
3.	Department of Mathematics, East China Normal University, Shanghai 200062

Received May 2005 Revised November 2005 Published July 2007

Abstract

We show that for small $\epsilon>0$, the boundary blow-up problem

$-\epsilon^2\Delta u= u (u-a(x))(1-u) \mbox{ in } \Omega, u|_{\partial\Omega}=\infty$

has solutions with sharp interior layers and spikes, apart from boundary layers. We also determine the location of these layers and spikes.

Keywords: spike layer, reduction method., bistable, boundary blow-up, Boundary and interior layer.

Mathematics Subject Classification: 35J20, 35J6.

Citation: Yihong Du, Zongming Guo, Feng Zhou. Boundary blow-up solutions with interior layers and spikes in a bistable problem. Discrete & Continuous Dynamical Systems - A, 2007, 19 (2) : 271-298. doi: 10.3934/dcds.2007.19.271

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American Institute of Mathematical Sciences