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|Title:||Existence and stability of multiple spot solutions for the Gray-Scott model in R^2$|
|Keywords:||Pattern formation; Self-replication;;Spotty solutions; Reaction-diffusion systems|
|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:||Mathematical Science|
Dept of Mathematics Research Papers
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