Stationary and Nonstationary Problems of Active Shielding

The problem of active shielding of some domains from the effect of the sources distributed in other domains is considered. The problem can be formulated either in a bounded domain or in an unbounded domain. The active shielding is realized via the implementation of additional sources in such a way that the total contribution of all sources leads to the desirable effect. Mathematically the problem is reduced to the search of the source terms satisfying some a priori described requirements to the solution and belongs to the class of inverse source problems. From the application standpoint, this problem can closely be related to the active shielding of noise, active vibration control and active scattering. It is important to note that along with undesirable field (noise) to be shielded the presence of a desirable component is accepted in the analysis. The solution of the problem requires only the knowledge of the total field on the perimeter of the shielded domain. This is the first publication where the solution of the problem is proved in general nonstationary linear and stationary nonlinear formulations. The examples of acoustic and Maxwell equations are considered.