Characteristic frequencies of bodies with thin spikes. I: Convergence and estimates

DOI10.1007/BF01209080zbMath0829.35088MaRDI QIDQ1896976

Rustem R. Gadyl'shin

Publication date: 12 September 1995

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

multiplicitiescharacteristic frequenciescharacteristic oscillationsNeumann and Dirichlet problemsperturbed and limit problemsscattering frequencies for an acoustic resonator

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (10)

Norm resolvent convergence of elliptic operators in domains with thin spikes ⋮ On the convergence of a nonlinear boundary-value problem in a perforated domain ⋮ Acoustic passive cloaking using thin outer resonators ⋮ Perfect transmission invisibility for waveguides with sound hard walls ⋮ Abnormal transmission of elastic waves through a thin ligament connecting two planar isotropic waveguides ⋮ Perturbation of the Steklov problem on a small part of the boundary ⋮ Waveguide with double threshold resonance at a simple threshold ⋮ Anomalies of acoustic wave propagation in two semi-infinite cylinders connected by a flattened ligament ⋮ Asymptotic behaviour of the Steklov spectrum on dumbbell domains ⋮ Localization of eigenfunctions of the Laplace operator in a domain with a perforated barrier

Cites Work

• Characterization of the eigenfunctions in the singularly perturbed domain
• Decomposition of series of resonances on a 'nonphysical' sheet
• A comparison of three perturbation methods for non-linear hyperbolic waves
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