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http://bura.brunel.ac.uk/handle/2438/557
Title: | Asymmetric patterns for the Gierer-Meinhardt system |
Authors: | Winter, M Wei, J |
Keywords: | Asymmetric patterns; Pattern formation; Mathematical biology; Singular perturbation;Weak Coupling |
Issue Date: | 2004 |
Publisher: | Elsevier |
Citation: | J Math Pures Appl 83: 358-390 |
Abstract: | In this paper, we rigorously prove the existence and stability of K-peaked asymmetric patterns for the Gierer-Meinhardt system in a two dimensional domain which are far from spatial homogeneity. We show that given any positive integers k_1,\,k_2 \geq 1 with k_1+k_2=K, there are asymmetric patterns with k_1 large peaks and k_2 small peaks. Most of these asymmetric patterns are shown to be unstable. However, in a narrow range of parameters, asymmetric patterns may be stable (in contrast to the one-dimensional case). |
URI: | http://www.elsevier.com/wps/find/journaldescription.cws_home/600731/description#description http://bura.brunel.ac.uk/handle/2438/557 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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28-gmas11.pdf | 317.54 kB | Adobe PDF | View/Open |
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