Asymptotic expansions of eigenvalues and eigenfunctions for elliptic boundary-value problems with rapidly oscillating coefficients in a perforated cube

DOI10.1007/BF02368668zbMath0844.35072OpenAlexW2328215061MaRDI QIDQ1910255

T. A. Mel'nik

Publication date: 21 May 1996

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02368668

zbMATH Keywords

complete asymptotic expansions\(\varepsilon\)-periodic coefficients

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Asymptotic expansions of solutions to PDEs (35C20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items

Asymptotics of eigenelements to spectral problem in thick cascade junction with concentrated masses ⋮ Simple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach ⋮ Asymptotic expansion of solution to Dirichlet problem in perforated domain: strange term case ⋮ Asymptotic approximations for solutions to quasilinear and linear parabolic problems with different perturbed boundary conditions in perforated domains ⋮ On a pore-scale stationary diffusion equation: scaling effects and correctors for the homogenization limit ⋮ Multiple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach

Cites Work

• Homogenization of elliptic eigenvalue problems. I
• Homogenization in open sets with holes
• Non-homogeneous media and vibration theory
• On the asymptotic behaviour at infinity of solutions in linear elasticity
• On the Convergence of the Energy, Stress Tensors, and Eigenvalues in Homogenization Problems of Elasticity
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