Geodesic
The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 3, pp. 354-366

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The model Neuman Laplacian in the system of two resonators, connected through a thin channel, is studied. The first terms of the asymptotic expansions of eigenvalues and eigenfunctions by small linking parameter are obtained. An explicit expression for resolvent is derived. The model problem is compared to a real one. 
@article{TMF_1994_100_3_a3,
     author = {A. A. Kiselev and B. S. Pavlov},
     title = {The eigenvalues and eigenfunctions of {Laplas} operator with {Neuman} boundary conditions in the system of two connected resonators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {354--366},
     publisher = {mathdoc},
     volume = {100},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a3/}
}
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A. A. Kiselev; B. S. Pavlov. The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 3, pp. 354-366. http://geodesic.mathdoc.fr/item/TMF_1994_100_3_a3/