Existence and stability of multiple-spot solutions for the Gray-Scott model in R-2
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AbstractIn 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. (C) 2002 Elsevier Science B.V All rights reserved.
All Author(s) ListWei JC, Winter M
Journal namePhysica D: Nonlinear Phenomena
Year2003
Month3
Day1
Volume Number176
Issue Number3-4
PublisherELSEVIER SCIENCE BV
Pages147 - 180
ISSN0167-2789
LanguagesEnglish-United Kingdom
Keywordspattern formation; reaction-diffusion systems; self-replication; spotty solutions
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED; Physics; Physics, Mathematical; PHYSICS, MATHEMATICAL; Physics, Multidisciplinary; PHYSICS, MULTIDISCIPLINARY

Last updated on 2020-20-10 at 00:25