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|Title: ||Existence and stability of multiple spot solutions for the Gray-Scott model in R^2$|
|Authors: ||Winter, M|
|Keywords: ||Pattern formation; Self-replication;|
Spotty solutions; Reaction-diffusion systems
|Publication Date: ||2003|
|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
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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