On the biharmonic scattering by impenetrable obstacles

In this paper, we consider the direct and inverse biharmonic obstacle scattering problems in both two and three dimensions with mainly the Dirichlet boundary condition being investgated. We first derive some basic properties for the biharmonic scattering solutions, which leads to a simple criterion for the uniqueness of the direct problem. Furthermore, a new type far-field pattern for biharmonic scattering is defined, and the correspondence between the far-field pattern and scattered field is proved. Then we derive the well-posedness of the direct problem by establishing the boundary integral equation method. Finally, the inverse problem for determining the obstacle is studied. Utilizing the reciprocity relations of the far-field pattern and scattered field, we show that the obstacle can be uniquely recovered from the measurements at a fixed frequency.