Asymptotics of eigenvalues with respect of a small parameter of singular perturbed boundary value problems for Laplacian in domains with narrow appendixes, connecting channels, slits, with exchanging of a type boundary conditions at small parts of boundaries and with frequently alternating changing of the boundary conditions are constructed. For Helmholtz resonators of the various types, the existence of poles with small imaginary parts for analytic continuations of solutions is proved. Asymtotics of these pole are constructed and treir resonant nature is shown. The existence of an analog of Helmholtz resonator in the hogomonization theo.
Main publications:
R.R. Gadylshin, “Suschestvovanie i asimptotiki polyusov s maloi mnimoi chastyu dlya rezonatora Gelmgoltsa”, Uspekhi matematicheskikh nauk, 52:1(313) (1997), 3–76
