On uniqueness in the problem of gravity-capillary water waves above submerged bodies
نویسندگان
چکیده
In this paper we consider the two-dimensional linear problem of wave–body interaction with surface tension effects being taken into account. We suggest a criterion for unique solvability of the problem based on symmetrization of boundary integral equations. The criterion allows us to develop an algorithm for detecting non-uniqueness (finding trapped modes) for given geometries of bodies; examples of numerical computation of trapped modes are given. We also prove a uniqueness theorem which provides simple bounds for the possible non-uniqueness parameters.
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