**Abstract : ** We will show in this talk how some models for the description of the interactions of waves with floating structures
can be formulated as hyperbolic initial boundary value problems or (depending on the model chosen for the propagation of the waves),
dispersive perturbations of such problems.
After recalling some classical results on hyperbolic initial boundary value problems (in particular on the nature of the admissible
boundary conditions), we will explain how the presence of a dispersive perturbation in the equations drastically changes the nature of
the equations. These
different behaviors raise several questions, one of which being nature of the dispersionless limit.
We will show that the presence of dispersive boundary layers make this limit singular, and explain how to control
them on an example motivated by a model for wave-structure interactions.