An inverse problem of reconstructing the refractive index interrain parabolic equations ^∗

Abstract

This work deals with an inverse problem of identifying the
refractive index in terrain parabolic equations, which has important
applications in radio systems and other applied scientific fields.
Unlike other inverse coefficient problems arising in the real field,
the underlying mathematical model is discussed in the complex field
which may lead to many mathematical tools not available, and the
corresponding theoretical analysis rather difficult. Based on the
optimal control framework, the recognition problem is transformed
into an optimization problem, and the existence and necessary
condition of the minimizer for the cost functional are deduced. The
local uniqueness and stability of the minimizer are derived from the
necessary condition. Finally, a gradient descent iterative scheme is
designed to solve the numerical solution of the inverse problem. The
validity of the proposed algorithm is illustrated by some typical
numerical examples.