The differential problem of active noise shielding

V. S. Ryaben'kii, S. V. Utyuzhnikov

Research output: Contribution to journalArticlepeer-review


The differential problem in active noise shielding (ANS), closely related to the active control of sound, is discussed. In ANS, some region are shielded from the influence of the remaining space by introducing additional sources. Malyuzhenets proposed an ANS solution based only on the total field given on the boundary of a shielded domain. He, along with Fedoryuk, also suggested the method of factorization of desired and noise components. A solution of the ANS problem for the Helmhotz equation was obtained with variable coefficients in the form of single-and-double-layer surface potentials. The solution of their study leads to surface potential for the Helmhotz equation and gives a general distribution of additional sources for the acoustic equations. This solution is based on the difference potential theory and is applicable to arbitrary domains, media, and boundary conditions. The ANS problem, which is linear and uniquely solvable, is solved in the general differential setting.

Original languageEnglish
Pages (from-to)357-359
Number of pages3
JournalDoklady Mathematics
Issue number3
Publication statusPublished - May 2006
Externally publishedYes


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