A Dirichlet-to-Neumann Map in the Study of a Floating Cylinder’s Small Oscillations.

We study a coupled PDE-ODE system modeling the small oscillations of a floating cylinder interacting with small water waves. The governing equations are formulated as an abstract wave-type equation on a suitable Hilbert space, and we establish the well-posedness of the associated initial value problem. A key element of the proof is the analysis of a partial Dirichlet-to-Neumann map on an unbounded domain with a non-smooth boundary.