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March  2006, 5(1): 85-95. doi: 10.3934/cpaa.2006.5.85

Spike solutions to a nonlocal differential equation

Changfeng Gui 1, and  Zhenbu Zhang 2,

1. 

Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-3009, Storrs, CT 06269-3009, United States
2. 

Department of Mathematics, Jackson State University, P.O. Box 17610, Jackson, MS 39217, United States

Received  March 2005 Revised  October 2005 Published  December 2005

In this paper we consider a nonlocal differential equation, which is a limiting equation of one dimensional Gierer-Meinhardt model. We study the existence of spike steady states and their stability. We also construct a single-spike quasi-equilibrium solution and investigate the dynamics of spike-like solutions.
Keywords: stability., spike solution, Gierer-Meinhardt model.
Mathematics Subject Classification: 35B25, 35B35, 35B40, 35K5.
Citation: Changfeng Gui, Zhenbu Zhang. Spike solutions to a nonlocal differential equation. Communications on Pure and Applied Analysis, 2006, 5 (1) : 85-95. doi: 10.3934/cpaa.2006.5.85
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