Geodesic
Barrier composed of perforated resonators and boundary conditions
Eurasian mathematical journal, Tome 15 (2024) no. 3, pp. 68-76

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the Laplace operator with the Neumann boundary condition in a two-dimensional domain divided by a barrier composed of many small Helmholtz resonators coupled with the both parts of the domain through small windows of diameter $2a$. The main terms of the asymptotic expansions in a of the eigenvalues and eigenfunctions are considered in the case in which the number of the Helmholtz resonators tends to innity. It is shown that such a homogenization procedure leads to some energy-dependent boundary condition in the limit. We use the method of matching the asymptotic expansions of boundary value problem solutions. 
@article{EMJ_2024_15_3_a6,
     author = {I. Y. Popov and E. S. Trifanova and A. S. Bagmutov and I. V. Blinova},
     title = {Barrier composed of perforated resonators and boundary conditions},
     journal = {Eurasian mathematical journal},
     pages = {68--76},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2024_15_3_a6/}
}
TY  - JOUR
AU  - I. Y. Popov
AU  - E. S. Trifanova
AU  - A. S. Bagmutov
AU  - I. V. Blinova
TI  - Barrier composed of perforated resonators and boundary conditions
JO  - Eurasian mathematical journal
PY  - 2024
SP  - 68
EP  - 76
VL  - 15
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2024_15_3_a6/
LA  - en
ID  - EMJ_2024_15_3_a6
ER  - 
%0 Journal Article
%A I. Y. Popov
%A E. S. Trifanova
%A A. S. Bagmutov
%A I. V. Blinova
%T Barrier composed of perforated resonators and boundary conditions
%J Eurasian mathematical journal
%D 2024
%P 68-76
%V 15
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2024_15_3_a6/
%G en
%F EMJ_2024_15_3_a6
I. Y. Popov; E. S. Trifanova; A. S. Bagmutov; I. V. Blinova. Barrier composed of perforated resonators and boundary conditions. Eurasian mathematical journal, Tome 15 (2024) no. 3, pp. 68-76. http://geodesic.mathdoc.fr/item/EMJ_2024_15_3_a6/