Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256717 | Wave Motion | 2018 | 11 Pages |
Abstract
In this work we construct and discuss special solutions of a homogeneous problem for the Laplace equation in a domain with cone-shaped boundaries. The problem at hand is interpreted as that describing oscillatory linear wave movement of a fluid under gravity in such a domain. These solutions are found in terms of the Mellin transform and by means of the reduction to some new functional-difference equations solved in an explicit form (by quadrature). The behavior of the solutions at large distances is studied by use of the saddle point technique. The corresponding eigenoscillations of a fluid are then interpreted as generalized eigenfunctions of the continuous spectrum.
Related Topics
Physical Sciences and Engineering
Earth and Planetary Sciences
Geology
Authors
Mikhail A. Lyalinov, Ksenia Sintsova,