On recovery of an inhomogeneous cavity in inverse acoustic scattering

Consider the time-harmonic acoustic scattering of an incident point source inside an inhomogeneous cavity. By constructing an equivalent integral equation, the well-posedness of the direct problem is proved in $L^p$ with using the classical Fredholm theory. Motivated by the previous work [ 10 ], a novel uniqueness result is then established for the inverse problem of recovering the refractive index of piecewise constant function from the wave fields measured on a closed surface inside the cavity.