Active control of sound with variable degree of cancellation

We formulate and solve a control problem for the field (e.g., time-harmonic sound) governed by a linear PDE or system on a composite domain in RnRn. Namely, we require that simultaneously and independently on each subdomain the sound generated in its complement be attenuated to a desired degree. This goal is achieved by adding special control sources defined only at the interface between the subdomains. We present a general solution for controls in the continuous and discrete setting.