Brunel University Research Archive(BURA) preserves and enables easy and open access to all
types of digital content. It showcases Brunel's research outputs.
Research contained within BURA is open access, although some publications may be subject
to publisher imposed embargoes. All awarded PhD theses are also archived on BURA.
Please use this identifier to cite or link to this item:
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 |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| FullText.pdf | 329.02 kB | Adobe PDF | View/Open |
Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.