Wave flows initiated by vertical lifting of a rectangular beam from shallow water

The problem of flows initiated by vertical lifting of a rectangular beam partially submerged in shallow water filling a rectangular prismatic channel with a horizontal bottom is studied in the long-wavelength approximation. The width of the beam is equal to the channel width, and its upper and lower planes are parallel to the channel bottom. In the first stage of the flow, the lower surface of the low beam is completely submerged in the liquid, which is lifted after it by hydrostatic pressure. Conditions for the well-posedness of this problem are obtained, and solutions describing the liquid flow in the region adjacent to the bottom surface of the beam and in outer regions with a free upper boundary are constructed for different laws of lifting of the beam.