2016/05/27 by Caro, Pedro, Helin, Tapio, Lassas, Matti · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1605.08710
In this paper we consider an inverse problem for the n-dimensional random Schrödinger equation (Δ-q+k2)u = 0. We study the scattering of plane waves in the presence of a potential q which is assumed to be a Gaussian random function such that its covariance is described by a pseudodifferential operator. Our main result is as follows: given the backscattered far field, obtained from a single realization of the random potential q, we uniquely determine the principal symbol of the covariance operator of q. Especially, for n=3 this result is obtained for the full non-linear inverse backscattering problem. Finally, we present a physical scaling regime where the method is of practical importance.