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http://bura.brunel.ac.uk/handle/2438/1063
Title: | Existence and stability of multiple spot solutions for the gray-scott model in R^2 |
Authors: | Winter, M Wei, J |
Keywords: | Pattern formation; Self-replication; Spotty solutions; Reaction-diffusion systems |
Issue Date: | 2005 |
Publisher: | World Scientific |
Citation: | Equadiff 2003, 813-818, World Scientific, Hackensack, NJ, 2005 |
Abstract: | We study the Gray-Scott model in a bounded two dimensional domain and establish the existence and stability of {\bf symmetric} and {\bf asymmetric} multiple spotty patterns. The Green's function and its derivatives together with two nonlocal eigenvalue problems both play a major role in the analysis. For symmetric spots, 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. For asymmetric spots, we show that they can be stable within a narrow parameter range. |
URI: | http://bura.brunel.ac.uk/handle/2438/1063 |
DOI: | https://doi.org/10.1142/9789812702067_0135 |
ISBN: | 981-256-169-2 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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