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Title: Symmetric and Asymmetric Multiple Clusters In a Reaction-Diffusion System
Authors: Winter, M
Wei, J
Keywords: Multiple clusters;singular perturbation;Turing instability
Issue Date: 2007
Publisher: Birkhaeuser, Basel
Citation: NoDEA Nonlinear differ. equ. appl. 14 (2007), 787-823
Abstract: We consider the Gierer-Meinhardt system in the interval (-1,1) with Neumann boundary conditions for small diffusion constant of the activator and finite diffusion constant of the inhibitor. A cluster is a combination of several spikes concentrating at the same point. In this paper, we rigorously show the existence of symmetric and asymmetric multiple clusters. This result is new for systems and seems not to occur for single equations. We reduce the problem to the computation of two matrices which depend on the coefficient of the inhibitor as well as the number of different clusters and the number of spikes within each cluster.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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