On Vibrating Thin Membranes with Mass Concentrated Near the Boundary: An Asymptotic Analysis

DOI10.1137/17M1118221zbMath1388.35184arXiv1705.02181OpenAlexW2963678234MaRDI QIDQ4565751

Luigi Provenzano, Matteo Dalla Riva

Publication date: 13 June 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.02181

zbMATH Keywords

eigenvaluesasymptotic analysisspectral analysismass concentrationSteklov boundary conditions

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) General topics in linear spectral theory for PDEs (35P05) Vibrations in dynamical problems in solid mechanics (74H45) Asymptotic expansions of solutions to PDEs (35C20) Membranes (74K15) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (3)

Membranes with thin and heavy inclusions: Asymptotics of spectra ⋮ On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set ⋮ Analytical and numerical assessments of boundary variations in Steklov eigenvalue problems

Cites Work

• Simple Neumann eigenvalues for the Laplace operator in a domain with a small hole
• Real analytic families of harmonic functions in a domain with a small hole
• Asymptotics for the spectrum of the Wentzell problem with a small parameter and other related stiff problems
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• Local problems for vibrating systems with concentrated masses: a review
• A few shape optimization results for a biharmonic Steklov problem
• Spectral geometry of the Steklov problem (survey article)
• Spectral stiff problems in domains surrounded by thin bands: asymptotic and uniform estimates for eigenvalues
• Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Generic Properties of Eigenfunctions
• Generic Properties of Eigenfunctions of Elliptic Partial Differential Operators
• ON VIBRATIONS OF A BODY WITH MANY CONCENTRATED MASSES NEAR THE BOUNDARY
• VIBRATIONS OF A MEMBRANE WITH MANY CONCENTRATED MASSES NEAR THE BOUNDARY
• Neumann to Steklov eigenvalues: asymptotic and monotonicity results
• ON VIBRATING MEMBRANES WITH VERY HEAVY THIN INCLUSIONS
• Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems
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