Multiscale Asymptotic Method for Steklov Eigenvalue Equations in Composite Media

Abstract

In this paper we consider the multiscale analysis of a Steklov eigenvalue equation with rapidly oscillating coefficients arising from the modeling of a composite media with a periodic microstructure. There are mainly two new results in the present paper. First, we obtain the convergence rate with $ \varepsilon^{1/2} $ for the multiscale asymptotic expansions of the eigenvalues and the eigenfunctions of the Steklov eigenvalue problem. Second, the boundary layer solution is defined. Numerical simulations are then carried out to validate the above theoretical results.