  We consider a diffusion-limited reaction in case the reacting entities are
not available simultaneously. Due to the fact that the reaction takes place
after a spatiotemporal accumulation of reactants, the underlying rate equation
has to be modified by additional non-local terms. Owing to the delay effects a
finite amount of reactants remains localized, preventing a further reaction and
the asymptotic decay is terminated at a finite density. The resulting
inhomogeneous non-zero stationary concentration is stable against long wave
length fluctuations. Below a critical wave vector $k_c$ the system becomes
inert, whereas a complete decay is realized above $k_c$. The phase diagram for
the one species-annihilation process $A + A \to 0$ exhibits a behavior
comparable to a second order phase transition. Obviously the memory effects are
equivalent to long range interaction and the non-local kinetics is basically
independent on space dimensions.
