International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 35630, 12 pages
doi:10.1155/IJMMS/2006/35630
On a singular integral equation with log kernel and its
application
Department of Mathematics, Jadavpur University, Kolkata 700032, India
Received 11 January 2005; Revised 12 June 2006; Accepted 21 June 2006
Copyright © 2006 Sudeshna Banerjea and Chiranjib Sarkar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We used function theoretic method to solve a singular integral
equation with logarithmic kernel in two disjoint finite intervals
where the unknown function satisfying the integral equation may be
bounded or unbounded at the nonzero finite endpoints of the
interval concerned. An appropriate solution of this integral
equation is then applied to solve the problem of scattering of
time harmonic surface water waves by a fully submerged thin
vertical barrier with a single gap.