Uniqueness in Determining a Ball with a Single Incoming Wave (Communications in Mathematical Research, 2019)
We prove that a ball with the impedance boundary condition is uniquely determined by the far-field pattern corresponding to an incident plane wave at one given wavenumber and one given incident direction. In the uniqueness proof, the impedance parameter in the impedance boundary condition is unknown.
Keywords: inverse obstacle scattering; uniqueness; ball; impedance boundary condition; Helmholtz equation