David Sher (DePaul University), Analysis Seminar

Title:  Eigenvalues of the sloshing problem

Abstract:  The sloshing problem describes small surface oscillations of an ideal fluid in a canal with sloping walls. Mathematically it corresponds to a mixed boundary value problem of Steklov-Neumann type. This boundary value problem has eigenvalues which correspond to the frequencies of sloshing oscillations. In 1983, Fox and Kuttler made a number of conjectures concerning the precise asymptotic behavior of these eigenvalues. We will outline an approach towards proving these conjectures, which has consequences for other mixed boundary value problems involving Steklov conditions. The talk is based on joint work in progress with M. Levitin (Reading), L. Parnovski (UCL) and I.Polterovich (Montreal).