Bulletin of the
Korean Mathematical Society BKMS

This paper is concerned with the long time behavior for the solution semiflow of the coupled two-compartment Gray-Scott equations with the homogeneous Neumann boundary condition on a bounded domain of space dimension $n\leq 3$. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the equations possesses a global attractor in $H^k(\Omega)^4$ $(k\geq 0)$ space.

Keywords: global attractor, two-compartment Gray-Scott equations, regularity estimates

MSC numbers: 35B40, 35B41, 35K20