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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.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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