Spectral asymptotics for a singularly perturbed fourth order locally\n periodic self-adjoint elliptic operator

2014/08/15 by Chechkina, Alexandra, Irina Pankratova, Pankratova, Irina +3
Computer Science · Engineering · Mathematics · #35B27 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1408.3627

openalex publication_date 2014/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the homogenization of a singularly perturbed self-adjoint fourth\norder elliptic equation with locally periodic coefficients, stated in a bounded\ndomain. We impose Dirichlet boundary conditions on the boundary of the domain.\nThe presence of large parameters in the lower order terms and the dependence of\nthe coefficients on the slow variable give rise to the effect of localization\nof the eigenfunctions. We show that the jth eigenfunction can be approximated\nby a rescaled function that is constructed in terms of the jth eigenfunction\nof fourth or second order order effective operators with constant coefficients,\ndepending on the large parameters.\n

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