The Lengyel-Epstein model for the CIMA reaction has the form
with the Neumann boundary condition. The authors give a detailed analysis of (1). Among others, they show: (i) System (1) has no nonconstant positive steady solution, if the size of the reactor, or the diffusion rate is not large enough. (ii) System (1) has non-constant positive steady solutions if the diffusion rate is large enough and the parameter lies in a suitable range.