Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/4531
Title: The Gierer-Meinhardt system on a compact two-dimensional Riemannian Manifold: Interaction of Gaussian curvature and Green's function
Authors: Tse, WH
Wei, J
Winter, M
Keywords: Pattern formation;Mathematical biology;Singular perturbation;Riemannian manifold
Issue Date: 2010
Publisher: Elsevier
Citation: Journal de Mathematiques Pures et Appliquees. 94(4): 366–397, Oct 2010
Abstract: In this paper, we rigorously prove the existence and stability of single-peaked patterns for the singularly perturbed Gierer-Meinhardt system on a compact two-dimensional Riemannian manifold without boundary which are far from spatial homogeneity. Throughout the paper we assume that the activator diffusivity is small enough. We show that for a threshold ratio of the activator diffusivity and the inhibitor diffusivity, the Gaussian curvature and the Green's function interact. A convex combination of the Gaussian curvature and the Green's function together with their derivatives are linked to the peak locations and the o(1) eigenvalues. A nonlocal eigenvalue problem (NLEP) determines the O(1) eigenvalues which all have negative part in this case.
URI: http://bura.brunel.ac.uk/handle/2438/4531
DOI: http://dx.doi.org/10.1016/j.matpur.2010.03.003
Appears in Collections:Mathematical Science
Dept of Mathematics Research Papers

Files in This Item:
File Description SizeFormat 
FullText.pdf401.55 kBAdobe PDFView/Open


Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.