Geodesic
Model of real-time active noise shielding of a given subdomain subject to external noise sources
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 480-491 
V. S. Ryaben'kii. Model of real-time active noise shielding of a given subdomain subject to external noise sources. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 480-491. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a6/
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     title = {Model of real-time active noise shielding of a~given subdomain subject to external noise sources},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Malyuzhinets G. D., “Nestatsionarnaya zadacha difraktsii dlya volnovogo uravneniya s kontaktnym nositelem pravoi chasti”, Tr. akustich. in-ta AN SSSR, 15, M., 1971, 124–139

[2] Fedoryuk M. V., “Nestatsionarnaya problema podavleniya shuma”, Akustich. zhurn., 22:3 (1976), 339–443

[3] Nelson P. A., Elliott S. J., Active control of sound, Acad. Press, San Diego, 1999

[4] Ryabenkii V. S., “Raznostnaya zadacha ekranirovaniya”, Funkts. analiz i ego prilozh., 29:1 (1995), 70–71 | MR

[5] Ryabenkii V. S., “Nelineinaya zadacha ekranirovaniya”, Uspekhi matem. nauk, 50:4 (1995), 146

[6] Veitsman R. I., Ryabenkii V. S., “Raznostnye zadachi ekranirovaniya i imitatsii”, Dokl. RAN, 354:2 (1997), 151–154 | MR

[7] Ryabenkii V. S., Metod raznostnykh potentsialov i ego prilozheniya, Fizmatlit, M., 2002

[8] Ryaben'kii V. S., Utyuznikov S. V., Turan A., “On the application of difference potential theory to active noise control”, Advances Appl. Math., 40:2 (2008) | MR

[9] Lim H., Utyuznikov S. V., Lam Y. et al., “An experimental validation of the active noise control method based on difference potential”, AIAA, 47:4 (2009), 874–887 | DOI

[10] Ryabenkii V. S., Utyuzhnikov S. V., Tsynkov S. V., “Raznostnaya zadacha podavleniya shuma i drugie zadachi aktivnogo upravleniya odnochastotnym zvukom v sostavnoi oblasti”, Dokl. RAN, 425:4 (2009), 456–458 | MR

[11] Utyuznikov S. V., “Generalized Calderon–Ryaben'kii's Potentials”, IMA J. Appl. Math., 74:1 (2009), 128–148 | DOI | MR

[12] Ryabenkii V. S., “Ideya ispolzovaniya slabogo shuma dlya upravleniya podavleniem silnogo shuma v ekraniruemoi podoblasti v realnom vremeni”, Dokl. RAN, 430:2 (2010) | MR