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Generalized eigenfunction expansions for conservative scattering problems with an application to water waves. (English) Zbl 1171.76007

A spectral description is given of wave phenomena in conservative bound media, which amounts to the fact that time-dependent waves can often be represented by a continuous superposition of time-harmonic waves. The concern in the paper is with the question of the perturbation of such a generalized eigenfunction expansion in the context of scattering problems. The approach is illustrated by the scattering of linear water waves by a floating body. Although the results are not new, the main improvement is to be found in the structure of the proof which makes a clear distinction between the properties related to the free problem, and those which involve the perturbation.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q35 PDEs in connection with fluid mechanics
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