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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/562

Title: Spikes for the two-dimensional Gierer-Meinhardt system: The weak coupling case
Authors: Winter, M
Wei, J
Keywords: Pattern formation; Mathematical biology; Singular perturbation
Weak coupling
Publication Date: 2001
Publisher: Springer
Citation: J Nonlinear Sci 11 (2001): 415-458
Abstract: In this paper, we rigorously prove the existence and stability of multiple-peaked patterns for the singularly perturbed Gierer-Meinhardt system in a two dimensional domain which are far from spatial homogeneity. The Green's function together with its derivatives is linked to the peak locations and to the $o(1)$ eigenvalues, which vanish in the limit. On the other hand two nonlocal eigenvalue problems (NLEPs), one of which is new, are related to the O(1) eigenvalues. Under some geometric condition on the peak locations, we establish a threshold behavior: If the inhibitor diffusivity exceeds the threshold then we get stability, if it lies below then we get instability.
URI: www.springerlink.com
http://bura.brunel.ac.uk/handle/2438/562
Appears in Collections:Mathematics
School of Information Systems, Computing and Mathematics Research Papers

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