Exact internal controllability of Maxwell’s equations

Abstract

We consider the exact controllability of Maxwell's equations in a general region. Combining the frequency domain condition developed recently by Liu [11] and the multiplier techniques, we show that the system has exact internal controllability when the control is distributed and acts in an e-neighborhood of the boundary.

Internal stabilization of Maxwell′s equations inheterogeneous media

“…The exact boundary controllability and stabilization of Maxwell's equations have been studied by many authors [4,6,7,8,10,13,15,17,18,19,21] and are usually based on an observability estimate obtained by different methods like the multiplier method, microlocal analysis, the frequency domain method. A similar strategy leads to the internal controllability of Maxwell's equations, see for instance [17,18,22,23].…”

On the spectrum of Euler–Bernoulli beam equation with Kelvin–Voigt damping

“…This passive method, on the one hand, makes the distributed control practically applicable but on the other hand, brings some new mathematical challenges which attract an increasing research interests [6,22,23]. For the controllability study of this kind of systems, we refer to [16,17,[20][21][22][23]35]. The results of exponential stability by bounded viscous damping can be found in [3,6,10,29,39].…”

Boundary observability of a numerical approximation scheme of Maxwell’s system in a cube

“…Usually these results are based on an observability estimate guaranteeing that the total energy of solutions can be estimated in terms of some local measurements. A similar strategy leads to the internal controllability or stability of Maxwell's equations, see for instance [28,29,35,36].…”