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Scattering of tidal waves by reefs and spits

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  26 February 2010

P. A. Krutitskii
P. A. Krutitskii
Affiliation:
Department of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia.
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Abstract

The problem of scattering of tidal waves by reefs and spits of arbitrary shape is reduced to a skew derivative problem for the two-dimensional Helmholtz equation in the exterior of open arcs in a plane. The resulting boundary-value problem is studied by potential theory and a boundary integral equation method. After some transformations, the skew derivative problem is reduced to a Fredholm integral equation of the second kind, which is uniquely solvable. In this way the solvability theorem is proved and an integral representation of the solution is obtained. A uniqueness theorem is also proved.

MSC classification

Secondary: 35J25: Boundary value problems for second-order elliptic equations
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 355 - 370
Copyright
Copyright © University College London 2000

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