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|Title: ||Spikes for the Gierer-Meinhardt system in two dimensions: The strong coupling case|
|Authors: ||Winter, M|
|Keywords: ||Pattern formation; Mathematical biology; Singular perturbation|
|Publication Date: ||2002|
|Citation: ||J Differential Equations 178(2002): 478-518|
|Abstract: ||Numerical computations often show that the Gierer-Meinhardt system has stable
solutions which display patterns of multiple interior peaks
(often also called spots). These patterns are also frequently observed
in natural biological systems.
It is assumed that the
diffusion rate of the activator is very small and the
diffusion rate of the inhibitor is
finite (this is the so-called strong-coupling case).
In this paper, we rigorously
establish the existence and stability of such
solutions of the full Gierer-Meinhardt system in two dimensions
far from homogeneity.
Green's function together with its derivatives plays
a major role.|
|Appears in Collections:||Mathematical Science|
Dept of Mathematics Research Papers
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