High frequency asymptotic analysis of a string with rapidly oscillating density

DOI10.1017/S0956792500004307zbMath0983.34078MaRDI QIDQ2709834

Carlos Castro, Enrique Zuazua

Publication date: 10 April 2002

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemsingular perturbationasymptotic expansioneigenvalue problemhomogenizationWKB methodperiodic structuremultiple scales

Mathematics Subject Classification ID

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Linear boundary value problems for ordinary differential equations (34B05) Asymptotic expansions of solutions to ordinary differential equations (34E05) Multiple scale methods for ordinary differential equations (34E13)

Related Items (13)

Membranes with thin and heavy inclusions: Asymptotics of spectra ⋮ Higher order asymptotic homogenization for dynamical problems ⋮ Uniform boundary controllability and homogenization of wave equations ⋮ The string of variable density: perturbative and non-perturbative results ⋮ Convergence rate for some quasilinear eigenvalues homogenization problems ⋮ The string of variable density: further results ⋮ Estimates of eigenvalues and eigenfunctions in elliptic homogenization with rapidly oscillating potentials ⋮ High-frequency spectral analysis of thin periodic acoustic strips: Theory and numerics ⋮ On the finite-time stabilization of some hyperbolic control systems by boundary feedback laws: Lyapunov approach ⋮ Homogenization of Steklov eigenvalues with rapidly oscillating weights ⋮ Multiscale numerical algorithms for elastic wave equations with rapidly oscillating coefficients ⋮ Some remarks on homogenization and exact boundary controllability for the one-dimensional wave equation ⋮ A perturbative approach to the spectral zeta functions of strings, drums, and quantum billiards

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