The stability estimates in two-dimensional cloaking problem (Q2795492)

In this work, the authors consider a two-dimensional inverse electromagnetic scattering problem. The electromagnetic scattering problem describes the scattering of E-polarized electromagnetic waves in an infinite homogeneous medium. The main goal of this work is to study uniqueness and stability of the solution of a control problem where the control is through boundary conductivity. At first, the authors proved the existence and uniqueness of the weak solution of the direct problem. Next, they derived an a priori estimate for the solution of the direct problem. Then the authors went on to show the solvability of the control problem and derived the optimality system. Uniqueness and stability of optimal solutions with respect to small perturbations of both the cost functional and the incident wave are established.