Singular integral equations arising in water wave problems

Aloknath Chakrabarti

Mathematics Dept, Indian Institute of Science, Bangalore

Mixed Boundary Value Problems occur, in a natural way, in varieties of branches of physics and engineering and several mathematical methods have been developed to solve this class of problems of applied mathematics. While understanding applications of such boundary value problems are of immense value to physicists and engineers, analyzing these problems mathematically and determining their solutions by utilizing the most appropriate analytical or numerical methods are the concerns of applied mathematicians. Of the various analytical methods, which are useful to solve certain mixed boundary value problems arising in the theory of scattering of surface water waves, the methods involving complex function theory and singular integral equations will be examined in detail along with some recent developments of such methods.

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