A criterion for the existence of decaying solutions in the problem on a resonator with a cylindrical waveguide
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Publication:2498291
DOI10.1007/s10688-006-0016-1zbMath1162.35342OpenAlexW2321621797MaRDI QIDQ2498291
Publication date: 16 August 2006
Published in: Functional Analysis and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10688-006-0016-1
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Antennas, waveguides in optics and electromagnetic theory (78A50)
Related Items (18)
From zero transmission to trapped modes in waveguides ⋮ Finite-dimensional approximations of the Steklov-Poincaré operator for the Helmholtz equation in periodic waveguides ⋮ Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide ⋮ Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold ⋮ Curved channels with constant cross sections may support trapped surface waves ⋮ Almost standing waves in a periodic waveguide with resonator, and near-threshold eigenvalues ⋮ The Mandelstam energy radiation conditions and the Umov-Poynting vector in elastic waveguides ⋮ Discrete spectrum of cross-shaped quantum waveguides ⋮ Discrete spectrum of cranked, branching, and periodic waveguides ⋮ Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide ⋮ Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides ⋮ Transmission conditions in one-dimensional model of a rectangular lattice of thin quantum waveguides ⋮ Scheme for interpretation of approximately computed eigenvalues embedded in a continuous spectrum ⋮ Criteria for trapped modes in a cranked channel with fixed and freely floating bodies ⋮ Eigenvalues of the Laplace operator with the Neumann conditions at regular perturbed walls of a waveguide ⋮ Finite-dimensional approximations to the Poincaré–Steklov operator for general elliptic boundary value problems in domains with cylindrical and periodic exits to infinity ⋮ The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides ⋮ Criteria for the absence and existence of bounded solutions at the threshold frequency in a junction of quantum waveguides
Cites Work
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