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DC Field | Value | Language |
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dc.contributor.author | Tse, WH | - |
dc.contributor.author | Wei, J | - |
dc.contributor.author | Winter, M | - |
dc.date.accessioned | 2010-09-01T09:57:54Z | - |
dc.date.available | 2010-09-01T09:57:54Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Journal de Mathematiques Pures et Appliquees. 94(4): 366–397, Oct 2010 | en |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/4531 | - |
dc.description.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. | en |
dc.description.sponsorship | RGC of Hong Kong | en |
dc.language.iso | en | en |
dc.publisher | Elsevier | en |
dc.relation.uri | http://www.sciencedirect.com/science/article/pii/S002178241000036X | en |
dc.subject | Pattern formation | en |
dc.subject | Mathematical biology | en |
dc.subject | Singular perturbation | en |
dc.subject | Riemannian manifold | en |
dc.title | The Gierer-Meinhardt system on a compact two-dimensional Riemannian Manifold: Interaction of Gaussian curvature and Green's function | en |
dc.type | Article | en |
dc.identifier.doi | http://dx.doi.org/10.1016/j.matpur.2010.03.003 | - |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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