Existence and Stability of Multiple Spot Solutions for the Gray-scott Model in R2
نویسنده
چکیده
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 together with its derivatives and two nonlocal eigenvalue problems both play a major role in the analysis. We establish a threshold behavior: If a certain inequality holds then we get stability, otherwise we get instability of multiple spot solutions. The exact asymptotics of the critical thresholds are obtained.
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