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Title: | Existence, classification and stability analysis of multiple-peaked solutions for the gierer-meinhardt system in R^1 |
Authors: | Winter, M Wei, J |
Keywords: | Stability;Multiple-peaked solutions;Singular perturbations;Turing's instability |
Issue Date: | 2007 |
Publisher: | Project Euclid |
Citation: | Methods and Applications of Analysis. 14 (2) 119-164 |
Abstract: | We consider the Gierer-Meinhardt system in R^1. where the exponents (p, q, r, s) satisfy 1< \frac{ qr}{(s+1)( p-1)} < \infty, 1 <p < +\infty, and where \ep<<1, 0<D<\infty, \tau\geq 0, D and \tau are constants which are independent of \ep. We give a rigorous and unified approach to show that the existence and stability of N-peaked steady-states can be reduced to computing two matrices in terms of the coefficients D, N, p, q, r, s. Moreover, it is shown that N-peaked steady-states are generated by exactly two types of peaks, provided their mutual distance is bounded away from zero. |
URI: | http://bura.brunel.ac.uk/handle/2438/2970 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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42-Npeak1d8.pdf | 352.84 kB | Adobe PDF | View/Open |
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