Contribution to the theory of diffusion-reaction controlled Liesegang patterns

A Turing-type reaction-diffusion model is explored which may be applicable to Liesegang bands, rings, and spirals evolving by precipitation in the environs of an equilibrium solubility product relation. Because of their incompletely specified initial and (or) boundary conditions the solutions exhibit a bivariate free boundary degeneracy. We find that one degree of freedom may be removed by the specification of a global rate constant and the other by the specification of a principle of optimal wave number selection within linear stability theory. Existence conditions for banding in one dimension are established and these agree with particular observations.