On a singular integral equation with log kernel and its application

Sudeshna Banerjea, Chiranjib Sarkar
2006 International Journal of Mathematics and Mathematical Sciences  
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.
doi:10.1155/ijmms/2006/35630 fatcat:7cw6cnqumza4lo6pmsqc7shica