Abstract
Three initial-boundary value problems for Sobolev's equation which describes the propagation of non-stationary internal waves in a channel with an exponentially stratified liquid have been studied. Waves are excited as a consequence of the small vibrations of one of the following three vertical structures set up in the channel: a barrier placed on the bottom of the channel, two barriers touching the walls of the channel and forming a diaphragm, and “baffles” which do not touch the walls. An explicit solution is constructed for each problem, its behaviour is studied at large times and the phenomena associated with the singularities of the velocity field of the fluid particles are investigated.
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