We analyze the management of a coastal aquifer under seawater intrusion using distributed control methods. The aquifer's state is taken as the water head elevation, which varies with time and in space since extraction, natural recharge and lateral water flows vary with time and in space. The water head, in turn, induces a temporal-spatial seawater intrusion process, which changes the volume of fresh water in the aquifer. Under reasonable conditions we show that the optimal state converges to a steady state process that is constant in time. We characterize the optimal steady state process in terms of a standard control problem (in space) and offer a tractable algorithm to solve for it.