Inverse scattering for the biharmonic wave equation with a random potential

Abstract

We consider the inverse random potential scattering problem for the two-and threedimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of the work are twofold. First, the unique continuation principle is proved for the fourth order biharmonic wave equation with rough potentials and the well-posedness of the direct scattering problem is established in the distribution sense. Second, the correlation strength of the random potential is shown to be uniquely determined by the high frequency limit of the second moment of the scattered field averaged over the frequency band. Moreover, we demonstrate that the expectation in the data can be removed and the data of a single realization is sufficient for the uniqueness of the inverse problem with probability one when the medium is lossless. PEIJUN LI AND XU WANGThe potential ρ is assumed to be a Gaussian random field defined in a complete probability space (Ω, F, P), where P is the probability measure. More precisely, ρ is required to satisfy the following assumption (cf. [15]).