  This paper addresses an inverse cavity scattering problem associated with the
biharmonic wave equation in two dimensions. The objective is to determine the
domain or shape of the cavity. The Green's representations are demonstrated for
the solution to the boundary value problem, and the one-to-one correspondence
is confirmed between the Helmholtz component of biharmonic waves and the
resulting far-field patterns. Two mixed reciprocity relations are deduced,
linking the scattered field generated by plane waves to the far-field pattern
produced by various types of point sources. Furthermore, the symmetry relations
are explored for the scattered fields generated by point sources. Finally, we
present two uniqueness results for the inverse problem by utilizing both
far-field patterns and phaseless near-field data.
