  The results in \cite{O2} (see \cite{O1} for the quasistatics regime) consider
the Helmholtz equation with fixed frequency $k$ and, in particular imply that,
for $k$ outside a discrete set of resonant frequencies and given a source
region $D_a\subset \mathbb{R}^{d}$ ($d=\overline{2,3}$) and $u_0$, a solution
of the homogeneous scalar Helmholtz equation in a set containing the control
region $D_c\subset \mathbb{R}^{d}$, there exists an infinite class of boundary
data on $\partial D_a$ so that the radiating solution to the corresponding
exterior scalar Helmholtz problem in $\mathbb{R}^{d} \setminus D_a$ will
closely approximate $u_0$ in $D_c$. Moreover, it will have vanishingly small
values beyond a certain large enough "far-field" radius $R$.
  In this paper we study the minimal energy solution of the above problem (e.g.
the solution obtained by using Tikhonov regularization with the Morozov
discrepancy principle) and perform a detailed sensitivity analysis. In this
regard we discuss the stability of the the minimal energy solution with respect
to measurement errors as well as the feasibility of the active scheme (power
budget and accuracy) depending on: the mutual distances between the antenna,
control region and far field radius $R$, value of regularization parameter,
frequency, location of the source.

Analysis of PDEs