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Scattering of tidal waves by reefs and spits
Author(s) -
Krutitskii P. A.
Publication year - 2000
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015953
Subject(s) - mathematics , helmholtz equation , fredholm integral equation , uniqueness theorem for poisson's equation , mathematical analysis , skew , green's theorem , integral equation , boundary value problem , uniqueness , fundamental theorem of calculus , picard–lindelöf theorem , fixed point theorem , physics , astronomy
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.