The asymptotic behavior as ttoinfty of the solution of an initial-boundary value problem in the theory of internal waves

Summary (translated from the Russian): "We study the properties of a solution of the first initial-boundary value problem in the half-space {bf R}_+^3={x: (x_1,x_2)in{bf R}^2, x_3>0}, t>0, for the gravitationally gyroscopic wave equation {partial^2over{partial t^2}}(Delta-beta^2)u+bigg [N^2Delta_2+omega^2bigg ({partial^2over {partial x_3^2}}-beta^2bigg )bigg ]u=0, where N, omega, and beta are, respectively, the Brunt-Väisälä frequency, the Coriolis parameter and a parameter that characterizes the distribution of the density. Under definite conditions in the initial conditions the order of decrease of a solution is O(1/t) as ttoinfty, and we obtain an asymptotic expansion for this solution uniformly for all xin Ksubset{bf R}_+^3, where K is compact." par {Delta is the Laplacian in x_1,x_2,x_3 and Delta_2 indicates the Laplacian in the two variables x_1,x_2 only.}