Sloshing problem in a half-plane covered by a dock with two gaps: monotonicity and asymptotics of eigenvalues

Abstract

The two-dimensional sloshing problem is considered in a half-plane covered by a rigid dock with two symmetric gaps. It is proved that the antisymmetric (symmetric) sloshing eigenvalues are monotonically decreasing (increasing) functions of spacing between gaps and formulae for their derivatives are obtained.