Solving fully nonlinear fluid flow problems in channels having arbitrary bottom topography

Aloknath Chakrabarti

Mathematics Dept, Indian Institute of Science, Bangalore


A class of fully nonlinear fluid flow problems is examined for their mathematical solutions by the aid of singular integral equations .The original nonlinear boundary value problems are formulated in terms of Dirichlet's problem for Laplace equation to be satisfied by the potential function governing the flow problems under consideration, which involves unknown boundaries to be determined along with the potential function. Finally these boundary value problems are shown to be amenable for their complete solution via integral equations of special types involving unknown curves of integration, which can also be determined fully.

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