Model of real-time active noise shielding of a given subdomain subject to external noise sources

A linear one-dimensional problem is considered, which is interpreted as a mathematical model of sound propagation. Additional sound sources are constructed that shield a given subdomain from sound sources localized in an additional subdomain without changing the solution in the additional subdomain. A complicating point in the problem is that the desired shielding sources can be constructed at the current time as based only on information about the shielded process that has become available by this current time. In an important special case, information in a convenient form is derived via noise exploration introduced in this work.