Asymptotic behavior of the spectrum of certain problems, connected with the oscillation of fluids

Abstract

One obtains the principal term of the asymptotics of the spectrum in a series of problems of the theory of small oscillations of fluids, filling partially a container. First one discusses a certain problem of general character, the “nonlocal Steklov type problem”. The considered problems are connected with the oscillations of a capillary ideal (or capillary stratified) fluid, of a heavy viscous fluid, of a capillary viscous fluid, and with the oscillations of a fluid in container with an elastic bottom.