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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/1063

Title: Existence and stability of multiple spot solutions for the gray-scott model in R^2
Authors: Winter, M
Wei, J
Keywords: Pattern formation; Self-replication; Spotty solutions; Reaction-diffusion systems
Publication Date: 2005
Publisher: World Scientific
Citation: Equadiff 2003, 813-818, World Scientific, Hackensack, NJ, 2005
Abstract: We study the Gray-Scott model in a bounded two dimensional domain and establish the existence and stability of {\bf symmetric} and {\bf asymmetric} multiple spotty patterns. The Green's function and its derivatives together with two nonlocal eigenvalue problems both play a major role in the analysis. For symmetric spots, we establish a threshold behavior for stability: If a certain inequality for the parameters holds then we get stability, otherwise we get instability of multiple spot solutions. For asymmetric spots, we show that they can be stable within a narrow parameter range.
URI: http://eproceedings.worldscinet.com/9789812702067/9789812702067.shtml
http://bura.brunel.ac.uk/handle/2438/1063
ISBN: 981-256-169-2
Appears in Collections:School of Information Systems, Computing and Mathematics Research Papers
Mathematical Science

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