Geodesic
Global dynamics of a reaction-diffusion system
Electronic journal of differential equations, Tome 2011 (2011)
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.
Classification : 37L30, 35B40, 35B41, 35K55, 35K57, 80A32, 92B05
Keywords: reaction-diffusion system, Brusselator, two-cell model, global attractor, absorbing set, asymptotic compactness, exponential attractor 
@article{EJDE_2011__2011__a32,
     author = {You,  Yuncheng},
     title = {Global dynamics of a reaction-diffusion system},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1221.37159},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a32/}
}
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You,  Yuncheng. Global dynamics of a reaction-diffusion system. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a32/