THREE-DIMENSIONAL PROBLEM OF UNSTEADY WAVE MOTIONS OF A LIQUID IN A REGION OF VARIABLE DEPTH.

The present paper is devoted to the investigation of wave motions of a liquid due to an initial perturbation of arbitrary form for particular angles of inclination of the floor. A complete system of eigenfunctions corresponding to the continuous and discrete spectra is found. The theorem of the expansion of an arbitrary absolutely integrable function with respect to the boundary values of the eigenfunctions is proved. An exact solution of the problem is obtained and its asymptotic analysis is carried out.