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http://bura.brunel.ac.uk/handle/2438/567
Title: | Existence and stability of multiple spot solutions for the Gray-Scott model in R^2$ |
Authors: | Wei, J |
Keywords: | Pattern formation; Self-replication;;Spotty solutions; Reaction-diffusion systems |
Issue Date: | 2003 |
Publisher: | Elsevier |
Citation: | Winter, M. and Wei, J. (2003) 'Existence and stability of multiple spot solutions for the Gray-Scott model in R^2$', Physica D: Nonlinear Phenomena, 176(3-4), pp. 147-180. doi:10.1016/S0167-2789(02)00743-1. |
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/567 |
DOI: | https://doi.org/10.1016/s0167-2789(02)00743-1 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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