Abstract In this paper, we consider the obstacle scattering problem for biharmonic wave equations with the Dirichlet boundary condition in both two and three dimensions. Firstly, some basic properties are derived for the scattered fields, which leads to a simple criterion for the uniqueness of the solution. Then a new definnition for the far-field pattern is introduced, where the correspondence between the far-field pattern and scattered field is established. With these preparations, we prove the existence of a unique solution in associated Sobolev spaces by the boundary integral equation method, which relies on a natural decomposition of the biharmonic operator and the theory of the pseudodifferential operator. Moreover, the inverse problem in determining the shape and location of the obstacle is studied. By establishing some novel reciprocity relations between the far-field pattern and the scattered field, we show that the obstacle can be uniquely recovered from the far-field measurements at two frequencies or near field measurements at a fixed frequency.
Wu et al. (Wed,) studied this question.