May  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

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

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.

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