Uniform attractor of non-autonomous three-component reversible Gray–Scott system

Abstract

We discuss the long time behavior of solutions for the non-autonomous three-component reversible Gray–Scott system with Dirichlet boundary condition on a bounded domain of space dimension n⩽3. When the external force is translation compact in appropriate space, we obtain the existence and the structure of the uniform attractor for the processes associated to the system by constructing skew product flow on the extended phase space. Also, we establish that there exists a unique bounded asymptotically stable solution to the system when the external forces are properly small.