Diffractive behavior of the wave equation in periodic media: weak convergence analysis
From MaRDI portal
Publication:842507
DOI10.1007/s10231-008-0089-yzbMath1200.35019OpenAlexW1974572452MaRDI QIDQ842507
Grégoire Allaire, Mariapia Palombaro, Jeffrey Rauch
Publication date: 25 September 2009
Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10231-008-0089-y
Singular perturbations in context of PDEs (35B25) Schrödinger operator, Schrödinger equation (35J10) Initial value problems for second-order hyperbolic equations (35L15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Geometric optics (78A05)
Related Items
Dispersive homogenized models and coefficient formulas for waves in general periodic media ⋮ Approximate normal forms via Floquet-Bloch theory: Nehorošev stability for linear waves in quasiperiodic media ⋮ Analysis of micro-structural effects on phononic waves in layered elastic media with periodic nonsmooth coordinates ⋮ Outgoing wave conditions in photonic crystals and transmission properties at interfaces ⋮ Homogenization and correctors for the wave equation with periodic coefficients ⋮ A two-scale model for the periodic homogenization of the wave equation ⋮ DIFFRACTION OF BLOCH WAVE PACKETS FOR MAXWELL'S EQUATIONS ⋮ Diffractive geometric optics for Bloch wave packets ⋮ Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media ⋮ DISPERSIVE EFFECTIVE MODELS FOR WAVES IN HETEROGENEOUS MEDIA ⋮ An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions ⋮ A corrector for a wave problem with periodic coefficients in a 1D bounded domain ⋮ Bloch-Wave Homogenization on Large Time Scales and Dispersive Effective Wave Equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Diffractive geometric optics for Bloch wave packets
- Homogenization of periodic systems with large potentials
- Dispersive limits in the homogenization of the wave equation.
- Correctors for the homogenization of the wave and heat equations
- Homogenization of the Schrödinger equation and effective mass theorems
- On Burnett coefficients in periodic media
- Parabolic Wave Equation Approximations in Heterogenous Media
- H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations
- A Dispersive Effective Medium for Wave Propagation in Periodic Composites
- Microlocal defect measures
- Homogenization and Two-Scale Convergence
- Oscillations and Energy Densities in the Wave Equation
- A General Convergence Result for a Functional Related to the Theory of Homogenization
- Boundary layer tails in periodic homogenization
- Dispersive nonlinear geometric optics
- Homogenization limits and Wigner transforms
- Homogenization of a Nonlinear Convection-Diffusion Equation with Rapidly Oscillating Coefficients and Strong Convection
- Floquet theory for partial differential equations
