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  • 1.
    Chechkina, Alexandra
    et al.
    Lomonosov Moscow State University, Moscow, Russia.
    Pankratova, Iryna
    Narvik University College, Narvik, Norway.
    Pettersson, Klas
    Narvik University College, Narvik, Norway.
    Spectral asymptotics for a singularly perturbed fourth order locally periodic elliptic operator2015In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576, Vol. 93, no 1-2, p. 141-160Article in journal (Refereed)
    Abstract [en]

    We consider the homogenization of a singularly perturbed self-adjoint fourth order elliptic operator with locally periodic coefficients, stated in a bounded domain. We impose Dirichlet boundary conditions on the boundary of the domain. The presence of large parameters in the lower order terms and the dependence of the coefficients on the slow variable lead to localization of the eigenfunctions. We show that the jth eigenfunction can be approximated by a rescaled function that is constructed in terms of the jth eigenfunction of fourth or second order effective operators with constant coefficients.

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