Wave interaction with two-dimensional bodies floating in a two-layer fluid: uniqueness and trapped modes

Existing results on the linearized water-wave problem for a homogeneous fluid are extended to the case of a two-layer fluid. In particular, the appropriate form of Mazʹyaʹs identity is presented and used to obtain results on the uniqueness of the solutions to forcing problems for a structure in a two-layer fluid. Further, examples of geometries are constructed for which trapped modes occur; such modes are finite-energy solutions of the unforced problem and provide examples of non-uniqueness.