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Mathematical analysis of guided water waves. (English) Zbl 0787.76007

Summary: The authors consider the problem of three-dimensional linear water waves that are guided along the coast. The problem is reduced to a two- dimensional eigenvalue problem for a family of unbounded selfadjoint operators with noncompact resolvent. Questions are investigated concerning the existence, number, and properties of the guided modes, with particular attention given to low- and high-frequency behaviour. The authors point out a large variety of results that greatly depend on the geometry of the bottom relief.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35P15 Estimates of eigenvalues in context of PDEs
86A05 Hydrology, hydrography, oceanography
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