Regularized solutions of a three-dimensional inverse scattering problem for the wave equation

Abstract

Using a variational method, the authors give regularized solutions to the problem of determining the index of refraction n in the inhomogeneous wave equation ( Delta +k2n2(x))u(x)=F(x) x in Omega where Omega is a domain in R3, and k>0 is given. It is assumed that a certain integral quantity, of the nature of a scattering amplitude, is known. Then a=n2 is to be determined in a compact subset of Linfinity ( Omega ), such that the given integral is closest to a 'measured' value h in R.