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.
S. Banerjea, “Scattering of water waves by a vertical wall with gaps,” Journal of Australian Mathematical Society. Series B, vol. 37, no. 4, pp. 512–529, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Banerjea and B. N. Mandal, “Scattering of water waves by a submerged thin vertical wall with a gap,” Journal of Australian Mathematical Society. Series B, vol. 39, no. 3, pp. 318–331, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Chakrabarti, S. R. Manam, and S. Banerjea, “Scattering of surface water waves involving a vertical barrier with a gap,” Journal of Engineering Mathematics, vol. 45, no. 2, pp. 183–194, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. Chakrabarti and L. Vijaya Bharathi, “Transmission of water waves through a gap in a submerged vertical barrier,” Indian Journal of Pure and Applied Mathematics, vol. 22, no. 6, pp. 491–512, 1991.
View at: Google ScholarS. R. Manam, “A logarithmic singular integral equation over multiple intervals,” Applied Mathematics Letters, vol. 16, no. 7, pp. 1031–1037, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet