This issuePrevious ArticleConcentrating phenomena in some elliptic Neumann problem: Asymptotic behavior of solutionsNext ArticleOn the Lyapunov dimension of cascade systems
In this work the existence of a global attractor for the solution semiflow of the
Gray-Scott equations with the Neumann boundary conditions on bounded domains
of space dimensions $n\leq 3$ is proved. This reaction-diffusion system does
not have dissipative property inherently due to the oppositely signed nonlinearity.
The asymptotical compactness is shown by a new decomposition method.
It is also proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite.