Homogenization method for problems on quasiclassical asymptotics

Wave equation (35L05) Averaging method for ordinary differential equations (34C29) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Cites Work

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Homogenization of the Poisson equation with Dirichlet conditions in random perforated domains
On the convergence of Bloch eigenfunctions in homogenization problems
Homogenization of hyperbolic equations
Homogenization of partial differential equations. Translated from the original Russian by M. Goncharenko and D. Shepelsky
Operator separation of variables for adiabatic problems in quantum and wave mechanics
Resonances in asymptotic solutions of the Cauchy problem for the Schrödinger equation with rapidly oscillating finite-zone potential
Non-homogeneous media and vibration theory
Homogenization in perforated domains beyond the periodic setting.
Einige Sätze über Kettenbrüche, mit Anwendungen auf die Theorie der Diophantischen Approximationen.
Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom
Approximate formulas for eigenvalues of the Laplace operator on a torus arising in linear problems with oscillating coefficients
Averaging of linear operators, adiabatic approximation, and pseudodifferential operators
Stochastic two-scale convergence and Young measures
On operator estimates in homogenization of nonlocal operators of convolution type
Homogenization of operators with perturbations of general form in the lower-order terms
Homogenization of elliptic difference operators
Operator estimates in homogenization theory
Periodic Homogenization of Nonlocal Operators with a Convolution-Type Kernel
Two-timing, variational principles and waves
Semiclassical approximation for equations with periodic coefficients
Homogenization of the Cauchy Problem for the Wave Equation with Rapidly Varying Coefficients and Initial Conditions
Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations
New integral representations of the Maslov canonical operator in singular charts
An Operator Calculus Having Applications in Quantum Electrodynamics
On operator estimates of the homogenization of higher-order elliptic systems
Spectral gaps for the linear water‐wave problem in a channel with thin structures
Multiscale model reduction. Multiscale finite element methods and their generalizations
Homogenization of hyperbolic equations: operator estimates with correctors taken into account
A Variational Theory of Convolution-Type Functionals
Homogenization for operators with arbitrary perturbations in coefficients
Operator-theoretic approach to the homogenization of Schrödinger-type equations with periodic coefficients

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