On direct and inverse spectral problems for sloshing of a two-layer fluid in an open container

Nikolay Kuznetsov

Published 2016-08-19Version 1

We study direct and inverse eigenvalue problems for a pair of harmonic functions with a spectral parameter in boundary and coupling conditions. The direct problem is relevant to sloshing frequencies of free oscillations of a two-layer fluid in a container. The upper fluid occupies a layer bounded above by a free surface and below by a layer of fluid of greater density. Both fluids are assumed to be inviscid, incompressible, and heavy, whereas the free surface and the interface between fluids are supposed to be bounded.