We consider the A + B --> 0 diffusion-controlled reaction under a stea
dy source of particle pairs, all generated with the same interparticle
distance. The pair creation stops after the time T. We monitor the re
laxation of the system and we present for 1d numerical and analytical
results. The decay form after the stop is strongly dependent on T and
thus the reaction-diffusion system keeps memory of the generation time
. We discuss also the situation in higher dimensions.