Geodesic
On scattering by cylinder with narrow slit and with shell of finite depth
Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 1, pp. 24-43

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The method of matching asymptotic expansions is applied to construction of asymptotics of poles for the Green function analytic continuation of a two-dimensional analog of Helmholtz resonator with a shell of a finite depth and with Neumann's boundary condition. The explicit formulae for the principle terms of asymptotics of poles, for corresponding generalized eigenfunctions and for solutions of scattering problem are obtained. 
@article{TMF_1996_106_1_a2,
     author = {R. R. Gadyl'shin},
     title = {On scattering by cylinder with narrow slit and with shell of finite depth},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {24--43},
     publisher = {mathdoc},
     volume = {106},
     number = {1},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_106_1_a2/}
}
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R. R. Gadyl'shin. On scattering by cylinder with narrow slit and with shell of finite depth. Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 1, pp. 24-43. http://geodesic.mathdoc.fr/item/TMF_1996_106_1_a2/