On direct and inverse obstacle scattering problems for biharmonic waves

Abstract In this paper the direct and inverse scattering problems for impenetrable obstacles in an infinite elastic Kirchhoff–Love two-dimensional plate are considered. By factoring the biharmonic operator, the displacement can be modeled by the Helmholtz equation and anti-Helmholtz equation with coupled boundary conditions. The well-posedness of the direct problem is proved by using a variational approach. The inverse problem consists of recovering the obstacle from the far field pattern of the scattered field at fixed wave number. The theoretical foundation of the linear sampling method is established. Numerical experiments show that the proposed method is feasible and effective.