Global dynamics of a reaction-diffusion system
In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled react...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2011-02-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/25/abstr.html |
| _version_ | 1818215027737362432 |
|---|---|
| author | Yuncheng You |
| author_facet | Yuncheng You |
| author_sort | Yuncheng You |
| collection | DOAJ |
| description | In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown. |
| first_indexed | 2024-12-12T06:29:33Z |
| format | Article |
| id | doaj.art-060c02088c8447e0afb008fa9ee8ea1a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T06:29:33Z |
| publishDate | 2011-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-060c02088c8447e0afb008fa9ee8ea1a2022-12-22T00:34:38ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-02-01201125,128Global dynamics of a reaction-diffusion systemYuncheng YouIn this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.http://ejde.math.txstate.edu/Volumes/2011/25/abstr.htmlReaction-diffusion systemBrusselatortwo-cell modelglobal attractorabsorbing setasymptotic compactnessexponential attractor |
| spellingShingle | Yuncheng You Global dynamics of a reaction-diffusion system Electronic Journal of Differential Equations Reaction-diffusion system Brusselator two-cell model global attractor absorbing set asymptotic compactness exponential attractor |
| title | Global dynamics of a reaction-diffusion system |
| title_full | Global dynamics of a reaction-diffusion system |
| title_fullStr | Global dynamics of a reaction-diffusion system |
| title_full_unstemmed | Global dynamics of a reaction-diffusion system |
| title_short | Global dynamics of a reaction-diffusion system |
| title_sort | global dynamics of a reaction diffusion system |
| topic | Reaction-diffusion system Brusselator two-cell model global attractor absorbing set asymptotic compactness exponential attractor |
| url | http://ejde.math.txstate.edu/Volumes/2011/25/abstr.html |
| work_keys_str_mv | AT yunchengyou globaldynamicsofareactiondiffusionsystem |