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http://bura.brunel.ac.uk/handle/2438/566| Title: | Asymmetric spotty patterns for the Gray-Scott model in R^2 |
| Authors: | Winter, M Wei, J |
| Keywords: | Asymmetric patterns; Spotty solutions;Self-replication; Reaction-diffusion system |
| Issue Date: | 2003 |
| Publisher: | Blackwell |
| Citation: | Winter, M. and Wei, J. (2003) 'Asymmetric spotty patterns for the Gray-Scott model in R^2', Studies in Applied Mathematics, 110(1), pp. 63-102. doi:10.1111/1467-9590.00231. |
| Abstract: | In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain. We show that given any two positive integers k_1,\,k_2, there are asymmetric solutions with k_1 large spots (type A) and k_2 small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetric solutions are shown to be unstable. However, in a narrow range of parameters, asymmetric solutions may be stable. |
| URI: | http://bura.brunel.ac.uk/handle/2438/566 |
| DOI: | https://doi.org/10.1111/1467-9590.00231 |
| Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| FullText.pdf | 306.75 kB | Adobe PDF | View/Open |
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