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|Title:||Asymmetric patterns for the Gierer-Meinhardt system|
|Keywords:||Asymmetric patterns; Pattern formation; Mathematical biology; Singular perturbation;Weak Coupling|
|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).|
|Appears in Collections:||Dept of Mathematics Research Papers|
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