Asymptotic Expansions of Eigenfunctions and Eigenvalues of the Steklov Spectral Problem in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions

Abstract

We consider a Steklov spectral problem for an elliptic differential equation with rapidly oscillating coefficients for thin perforated domains with rapidly varying thickness. We describe asymptotic algorithms for the solution of problems of this kind for thin perforated domains with different limit dimensions. We also establish asymptotic estimates for eigenvalues of the Steklov spectral problem for thin perforated domains with different limit dimensions. For certain symmetry conditions imposed on the structure of thin perforated domain and on the coefficients of differential operators, we construct and substantiate asymptotic expansions for eigenfunctions and eigenvalues.