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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
Issue Date: 2003
Publisher: Elsevier
Citation: Phys D 176: 147-180
Abstract: Existence and Stability of Multiple Spot Solutions for the Gray-Scott Model in $R^2$ In this paper, we rigorously prove the existence and stability of multiple spot patterns for the Gray-Scott system in a two dimensional domain which are far from spatial homogeneity. The Green's function and its derivatives together with two nonlocal eigenvalue problems both play a major role in the analysis. 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. The exact asymptotics of the critical thresholds are obtained.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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