Homogenization of spectral problem for locally periodic elliptic operators with signchanging density function
Abstract
The paper deals with homogenization of a spectral problem for a second order selfadjoint 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 1dimensional spectral problem and prove the convergence of spectra.
 Publication:

Journal of Differential Equations
 Pub Date:
 April 2011
 DOI:
 10.1016/j.jde.2011.01.022
 Bibcode:
 2011JDE...250.3088P