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, MWei, 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.shtmlhttp://bura.brunel.ac.uk/handle/2438/1063 ISBN: 981-256-169-2 Appears in Collections: MathematicsSchool of Information Systems, Computing and Mathematics Research Papers

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