  In this paper, we consider the obstacle scattering problem for biharmonic
equations with a Dirichlet boundary condition in both two and three dimensions.
Some basic properties are first derived for the biharmonic scattering
solutions, which leads to a simple criterion for the uniqueness of the direct
problem. Then a new type far-field pattern is introduced, where the
correspondence between the far-field pattern and scattered field is
established. Based on these properties, we prove the well-posedness of the
direct problem in associated function spaces by utilizing the boundary integral
equation method, which relys on a natural decomposition of the biharmonic
operator and the theory of the pseudodifferential operator. Furthermore, the
inverse problem for determining the obstacle is studied. By establishing some
novel reciprocity relations between the far-field pattern and scattered field,
we show that the obstacle can be uniquely recovered from the measurements at a
fixed frequency.
