Inverse Scattering for the Biharmonic Wave Equation with a Random Potential
Peijun Li, X.-B. Wang
Abstract
.We consider the inverse random potential scattering problem for the two- and three-dimensional 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 backscattering data 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.Keywordsinverse scatteringrandom potentialbiharmonic operatorpseudodifferential operatorprincipal symboluniquenessMSC codes35R3035R6060H15