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

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2007, Volume 19, Issue 2: 271-298. Doi: 10.3934/dcds.2007.19.271

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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
3.
Department of Mathematics, East China Normal University, Shanghai 200062

Received: April 30, 2005

Revised: October 31, 2005

Published: April 2007

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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.

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Mathematics Subject Classification: 35J20, 35J60.

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