# American Institute of Mathematical Sciences

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