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Homogenization of spectral problem for locally periodic elliptic operators with sign-changing density function
Narvik University College, Narvik, Norway; Ecole Polytechnique, Palaiseau Cedex, France.
Lebedev Physical Institute RAS, Moscow, Russia.
2011 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 250, no 7, p. 3088-3134Article in journal (Refereed) Published
Abstract [en]

The paper deals with homogenization of a spectral problem for a second order self-adjoint elliptic operator stated in a thin cylinder with homogeneous Neumann boundary condition on the lateral boundary and Dirichlet condition on the bases of the cylinder. We assume that the operator coefficients and the spectral density function are locally periodic in the axial direction of the cylinder, and that the spectral density function changes sign. We show that the behavior of the spectrum depends essentially on whether the average of the density function is zero or not. In both cases we construct the effective 1-dimensional spectral problem and prove the convergence of spectra.

Place, publisher, year, edition, pages
2011. Vol. 250, no 7, p. 3088-3134
Keywords [en]
Spectral problem, Sign-changing density, Homogenization, Thin cylinder
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-27157DOI: 10.1016/j.jde.2011.01.022OAI: oai:DiVA.org:hig-27157DiVA, id: diva2:1222154
Available from: 2018-06-21 Created: 2018-06-21 Last updated: 2018-06-21Bibliographically approved

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Pankratova, Iryna

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