We show analytically and numerically that a pail of uni-directionally
coupled spatially extended systems can synchronize. For the case of pa
rtial differential equations the synchronization can be achieved by ap
plying the scalar driving signals only at finite number of space point
s. Our approach is very general and can be useful for practical applic
ations since the synchronization is achieved via feeding in the respon
se system only the information from certain (discrete) spatial locatio
ns of the drive system. We also stress some open problems in the field
of synchronization of spatiotemporal chaos. (C) 1997 American Institu
te of Physics.