Splitting of resonant and scattering frequencies under shape deformation

DOI10.1016/j.jde.2004.02.017zbMath1121.35332OpenAlexW2039353458MaRDI QIDQ1881149

Faouzi Triki, Habib Ammari

Publication date: 4 October 2004

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.02.017

zbMATH Keywords

splittingLaplacian operatormultiple eigenvaluesboundary variationsgeneralized Rouche's theorem

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Perturbations in context of PDEs (35B20)

Related Items

Mathematical analysis of electromagnetic scattering by dielectric nanoparticles with high refractive indices ⋮ Asymptotic analysis of high-contrast phononic crystals and a criterion for the band-gap opening ⋮ Mathematical analysis of plasmonic resonances for nanoparticles: the full Maxwell equations ⋮ Asymptotic behaviors for eigenvalues and eigenfunctions associated to Stokes operator in the presence of small boundary perturbations ⋮ On the behavior of resonant frequencies in the presence of small anisotropic imperfections ⋮ On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions ⋮ Mathematical modeling of the photoacoustic effect generated by the heating of metallic nanoparticles ⋮ Perturbation of the scattering resonances of an open cavity by small particles. I: The transverse magnetic polarization case ⋮ Modal decompositions and point scatterer approximations near the Minnaert resonance frequencies ⋮ Asymptotic property for eigenelements of the Laplace operator in a domain with an oscillating boundary ⋮ Spectral analysis and stabilization of one dimensional wave equation with singular potential ⋮ Explicit terms in the small volume expansion of the shift of Neumann Laplacian eigenvalues due to a grounded inclusion in two dimensions ⋮ Layer potential techniques in spectral analysis. Part I: Complete asymptotic expansions for eigenvalues of the Laplacian in domains with small inclusions ⋮ Asymptotic Expansions for Eigenvalues of the Lamé System in the Presence of Small Inclusions ⋮ Asymptotic property and convergence estimation for the eigenelements of the Laplace operator ⋮ Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Partial differential equations. 2: Qualitative studies of linear equations
• Fifty years of eigenvalue perturbation theory
• Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain
• Asymptotic behaviour of the eigenvalues of the Dirichlet problem in a domain with a narrow slit
• Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator
• Existence of three-dimensional toroidal MHD equilibria with nonconstant pressure
• Boundary-variation solution of eigenvalue problems for elliptic operators.