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We study a flow of ultracold bosonic atoms through a one-dimensional channel that connects two macroscopic three-dimensional reservoirs of Bose-condensed atoms via weak links implemented as potential barriers between each of the reservoirs and the channel. We consider reservoirs at equal chemical potentials so that a superflow of the quasicondensate through the channel is driven purely by a phase difference 2Φ imprinted between the reservoirs. We find that the superflow never has the standard Josephson form ∼sin2Φ. Instead, the superflow discontinuously flips direction at 2Φ ¼ π and has metastable branches. We show that these features are robust and not smeared by fluctuations or phase slips. We describe a possible experimental setup for observing these phenomena.