Surface waves in a polygonal domain with Robin boundary conditions

A surface wave, propagating from infinity along a semi-infinite part, interacts with the impedance boundary of a 2D polygonal domain and gives rise to the reflected surface wave on this side and to the transmitted surface wave outgoing to infinity along the second semi-infinite side of the domain. The circular outgoing wave also propagates at infinity. It is shown that the classical solution of the problem is unique. By use of some known extension of the Sommerfeld-Malyuzhinets technique the problem at hand is reduced to functional Malyuzhinets equations and then to a system of integral equations of the second kind with the integral operator depending on a characteristic parameter. The integral equations are carefully studied. From the Sommerfeld integral representation of the solution the far field asymptotics is developed.