THE SOLUTION OF A CLASS OF BOUNDARY-VALUE PROBLEMS WITH SMOOTHLY VARYING BOUNDARY CONDITIONS
D. V. Evans · The Quarterly Journal of Mechanics and Applied Mathematics · 1985
A method is described for solving a particular boundary-value problem arising from the propagation of water waves through a region having continuously varying surface density. It is shown that similar boundary-value problems arising in other applications, in which one of the boundary conditions varies continuously in a specified manner along the boundary, and which reduces to a Wiener-Hopf problem in a limiting case, can also be solved explicitly by the method which involves the solution of a class of functional equations.