Global attractor of the Gray-Scott equations

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 <= 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.