Gadyl’shin, R. R. Splitting of the poles of a Helmholtz resonator. (English. Russian original) Zbl 0827.35095 Russ. Acad. Sci., Izv., Math. 43, No. 2, 233-260 (1994); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 5, 44-74 (1993). Summary: It is shown that in a neighborhood of a two-fold eigenvalue of the Neumann problem there are two poles of the Green’s function of the Helmholtz resonator. Asymptotic expressions for them with respect to a small parameter \(\varepsilon\) (the linear size of the hole) are constructed, and the principal terms of the asymptotics are written out for the corresponding scattering and radiation problems. Cited in 1 Document MSC: 35P25 Scattering theory for PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 78A45 Diffraction, scattering 70K30 Nonlinear resonances for nonlinear problems in mechanics 47A40 Scattering theory of linear operators Keywords:asymptotic expression; two-fold eigenvalue of the Neumann problem; Green’s function of the Helmholtz resonator PDFBibTeX XMLCite \textit{R. R. Gadyl'shin}, Russ. Acad. Sci., Izv., Math. 43, No. 2, 1 (1993; Zbl 0827.35095); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 5, 44--74 (1993) Full Text: DOI