On well-posedness of scattering problems in a kirchhoff–love infinite plate

We address scattering problems for impenetrable obstacles in an infinite elastic Kirchhoff–Love two-dimensional plate. The analysis is restricted to the purely bending case and the time-harmonic regime. Considering four types of boundary conditions on the obstacle, well-posedness for those problems is proved with the help of a variational approach: (i) for any wave number k when the plate is clamped, simply supported, or roller supported; (ii) for any k except a discrete set when the plate is free (this set is finite for convex obstacles).