International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 35630, 12 pages

On a singular integral equation with log kernel and its application

Sudeshna Banerjea and Chiranjib Sarkar

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.


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.