scientific article; zbMATH DE number 194901

Jacqueline Sanchez-Hubert, Enrique Sanchez-Palencia

Publication date: 5 June 1993

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Helmholtz equation continuous systems spectral theories Helmholtz-resonator large frequency phenomena linear vibration problems

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Thermodynamics in solid mechanics (74A15) Incompressible viscous fluids (76D99) Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids (74-02) Linear vibration theory (70J99) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99) Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems (70-02)

Related Items

Spectral gaps in a double-periodic perforated Neumann waveguide ⋮ Membranes with thin and heavy inclusions: Asymptotics of spectra ⋮ Domain derivative of the leading eigenvalue of a model transport operator ⋮ On the vibrations of a plate with a concentrated mass and very small thickness ⋮ Asymptotics of the principal eigenvalue of the Laplacian in 2D periodic domains with small traps ⋮ The stiff Neumann problem: Asymptotic specialty and “kissing” domains ⋮ Interaction of concentrated masses in a harmonically oscillating spatial body with Neumann boundary conditions ⋮ A Sufficient Condition for the Absence of Two-Dimensional Instabilities of an Elastic Plate in a Duct with Compressible Flow ⋮ Homogenization in perforated domains: a Stokes grill and an adsorption process ⋮ Range of the First Three Eigenvalues of the Planar Dirichlet Laplacian ⋮ Electromagnetic Steklov eigenvalues: existence and distribution in the self-adjoint case ⋮ Internal layer intersecting the boundary of a domain in a singular advection–diffusion equation ⋮ Asymptotic stability of the spectrum of a parametric family of homogenization problems associated with a perforated waveguide ⋮ A Novel Deep Neural Network Algorithm for the Helmholtz Scattering Problem In the Unbounded Domain ⋮ Mathematical Determination of the Fréchet Derivative with Respect to the Domain for a Fluid-Structure Scattering Problem: Case of Polygonal-Shaped Domains ⋮ Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part I: Generalized Fourier transform ⋮ Spectral Homogenization Problems in Linear Elasticity with Large Reaction Terms Concentrated in Small Regions of the Boundary ⋮ Étude numérique des pôles de résonance associés à la diffraction d'ondes acoustiques et élastiques par un obstacle en dimension 2 ⋮ About asymptotic approximations in thin waveguides ⋮ Eigenfrequency optimization in optimal design ⋮ Unnamed Item ⋮ Analysis of transient waves in thin structures utilizing matched asymptotic expansions ⋮ Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells ⋮ Fourier approach to homogenization problems ⋮ Attractors of parabolic problems with nonlinear boundary conditions. uniform bounds ⋮ Asymptotics of scattering frequencies with small imaginary parts for an acoustic resonator ⋮ Small oscillations of an ideal liquid contained in a vessel closed by an elastic circular plate, in uniform rotation ⋮ Asymptotics of the scattering frequencies for a thermoelasticity problem with small thermal conductivity ⋮ On propagation in an electromagnetic waveguide with concentrated dissipation ⋮ Homogenization for Alternating Boundary Conditions with Large Reaction Terms Concentrated in Small Regions ⋮ Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance ⋮ Modelisation of modulated vibration modes of repetitive structures ⋮ Unique identification of a multi-layered fluid-solid medium ⋮ Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition ⋮ Time Domain Integral Equation Methods in Computational Electromagnetism ⋮ A survey of finite element methods for time-harmonic acoustics ⋮ Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity ⋮ Vibrating systems with rigid light-weight inclusions: asymptotics of the spectrum and eigenspaces ⋮ Rigorous and heuristic treatment of certain sensitive singular perturbations ⋮ A justification of the method of junction of asymptotic expansions applied to a vibrating plate problem. Estimate of the impedance matrix ⋮ Compressibility and gravity effects in internal fluid-structure vibrations: basic equations and appropriate variational formulations ⋮ Optimal control of fluid equations with buoyancy ⋮ The performance of local absorbing boundary conditions for acoustic scattering from elliptical shapes ⋮ Variational-based reduced-order model in dynamic substructuring of coupled structures through a dissipative physical interface: recent advances ⋮ Systems of acoustic resonators in the quasistationary mode ⋮ Weakly singular Steklov condition in the multidimensional case ⋮ On the small oscillations of a catenoidal liquid drop between two parallel plates under zero gravity ⋮ Error estimates of the DtN finite element method for the exterior Helmholtz problem ⋮ On the study of small oscillations of two fluids occupying a bounded domain of arbitrary form ⋮ Asymptotics for the spectrum of the Wentzell problem with a small parameter and other related stiff problems ⋮ Time-domain formulation in computational dynamics for linear viscoelastic media with model uncertainties and stochastic excitation ⋮ Analytical study of the effect of wave number on the performance of local absorbing boundary conditions for acoustic scattering ⋮ Eigenoscillations of an elastic body with a rough surface ⋮ On spurious solutions in finite element approximations of resonances in open systems ⋮ Analysis of small oscillations of a heavy almost-homogeneous liquid-gas system ⋮ Interaction between thermoelastic and scalar oscillation fields ⋮ On scattering by a cylinder with a narrow slit and walls of finite thickness ⋮ Spectral study of a coupled compact-noncompact problem ⋮ A complete electromagnetic analog of the Helmholtz resonator ⋮ Concentrated forces. Asymptotic study ⋮ Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map ⋮ Asymptotics of the frequency of a surface wave trapped by a slightly inclined barrier in a liquid layer ⋮ Identification of the interface between acoustic and elastic waves from internal measurements ⋮ A controllability method with an artificial boundary condition for the exterior Helmholtz problem ⋮ On the controllability of an advection-diffusion equation with respect to the diffusion parameter: asymptotic analysis and numerical simulations ⋮ Mathematical study of the small oscillations of two nonmixing fluids, the lower inviscid, the upper viscoelastic, in an open container ⋮ Mathematical study of the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid and a barotropic gas (oscillations of a pendulum with almost homogeneous liquid and gas) ⋮ Analysis of the small oscillations of a system viscous liquid-barotropic gas in a container ⋮ Analysis of the small oscillations of two nonmixing fluids, the upper inviscid, the lower viscoelastic, in a fixed open container ⋮ Asymptotic approximation for the solution of a boundary-value problem with varying type of boundary conditions in a thick two-level junction ⋮ A spectral problem for the Laplacian in joined thin films ⋮ Solution of coupled acoustic-elastic wave propagation problems with anelastic attenuation using automatic \(hp\)-adaptivity ⋮ Electromagnetic scattering by small dielectric inhomogeneities. ⋮ Combined boundary integral equations for acoustic scattering-resonance problems ⋮ Sur un mouvement particulier d'un profil muni d'une cavité fermée par un couvercle élastique et remplie de liquide. (Particular motion of a profile with a cavity closed by an elastic cover and containing a liquid) ⋮ MODELING BONE CONDUCTION OF SOUND IN THE HUMAN HEAD: II. SIMULATION RESULTS ⋮ Modeling of bone conduction of sound in the human head using hp-finite elements: code design and verification ⋮ Approximation of a two dimensional problem of junctions ⋮ Homogenization of the Poisson equation in a thick periodic junction ⋮ Asymptotic modeling of the problem with contrasting stiffness ⋮ Homogenization and Bloch wave method for fluid tube bundle interaction ⋮ A Stiff Problem: Stationary Waves and Approximations ⋮ Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary ⋮ Mathematical Study of the Small Oscillations of a Pendulum Completely Filled with a Viscoelastic Fluid ⋮ Modeling of a singularly perturbed spectral problem by means of self-adjoint extensions of the operators of the limit problems ⋮ Gaps in the essential spectrum of periodic elastic waveguides ⋮ Mathematical and numerical modeling of plate dynamics with rotational inertia ⋮ On the rate of convergence for approximation of an eigenvalue problem describing vibrations of axisymmetric revolution elastic shells ⋮ Long time approximations for solutions of wave equations via standing waves from quasimodes ⋮ Various kinds of sensitive singular perturbations ⋮ Interactions of an elastic solid with a viscous fluid: Eigenmode analysis ⋮ A surface Helmholtz integral system for a sound radiation by an elastic body. A nonuniqueness theorem ⋮ Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity ⋮ Biot-pressure system with unilateral displacement constraints ⋮ On the perturbation of the electromagnetic energy due to the presence of small inhomogeneities ⋮ Homogenization of a boundary value problem with mixed type of boundary conditions in a thick junction ⋮ Long time approximations for solutions of wave equations associated with the Steklov spectral homogenization problems ⋮ Asymptotic analysis of an optimal control problem involving a thick two-level junction with alternate type of controls ⋮ Effective boundary conditions resulting from anisotropic and optimally aligned coatings: the two dimensional case ⋮ A two-scale model for the periodic homogenization of the wave equation ⋮ Spectral stiff problems in domains surrounded by thin bands: asymptotic and uniform estimates for eigenvalues ⋮ Mathematical study of the small oscillations of a spherical layer of viscous fluid about a rigid spherical core in the gravitational field ⋮ On the existence and the uniqueness of the solution of a fluid-structure interaction scattering problem ⋮ Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube ⋮ Mathematical study of the small oscillations of a spherical layer of viscoelastic fluid about a rigid spherical core in the gravitational field ⋮ Localization effect for Dirichlet eigenfunctions in thin non-smooth domains ⋮ Gradient damage analysis of a cylinder under torsion: bifurcation and size effects ⋮ Reduced models for modal analysis of fluid-structure systems taking into account compressibility and gravity effects ⋮ Asymptotic analysis of the high frequencies for the Laplace operator in a thin t-like shaped structure ⋮ Bloch wave homogenization of linear elasticity system ⋮ Asymptotic structure of the spectrum in a Dirichlet-strip with double periodic perforations ⋮ Bloch-wave homogenization for a spectral problem in fluid-solid structures ⋮ Newton’s Method for Convex Optimization ⋮ On the Maxwell's system in composite media ⋮ Semi-decentralized approximation of optimal control for partial differential equations in bounded domains ⋮ Formal asymptotics of eigenmodes for oscillating elastic spatial bodies with concentrated masses ⋮ Instabilities of Highly Anisotropic Spinning Disks ⋮ Asymptotic approximation of the solution of Stokes equations in a domain with highly oscillating boundary ⋮ An asymptotic study of a plate problem by a rearrangement method. Application to the mechanical impedance ⋮ A criterion for the existence of the essential spectrum for beak-shaped elastic bodies ⋮ Asymptotic behavior of eigenvalues of the Maxwell system in the presence of small changes in the interface of an inclusion ⋮ Boundary homogenization with large reaction terms on a strainer-type wall ⋮ On the characterization of the Fréchet derivative with respect to a Lipschitz domain of the acoustic scattered field ⋮ Hausdorff convergence and asymptotic estimates of the spectrum of a perturbed operator ⋮ On the existence of small oscillations of a liquid cylindrical column under zero gravity. I: The cylindrical container is fixed. ⋮ Two-scale convergence method and scattering problems ⋮ On vibrations of bodies with concentrated masses near boundaries ⋮ Guided waves in a moving layer of fluid between two elastic solids ⋮ Homogenization process of stratified masonry ⋮ The quasi-stationary mode of a Helmholtz resonator ⋮ New series of asymptotics of eigenvalues of the Sturm-Liouville problem with rapidly oscillating coefficients