On a Waveguide with Frequently Alternating Boundary Conditions: Homogenized Neumann Condition

摘要: We consider a waveguide modeled by the Laplacian in straight planar strip. The Dirichlet boundary condition is taken on upper boundary, while lower we impose periodically alternating and Neumann assuming period of alternation to be small. study case when homogenization gives instead ones. establish uniform resolvent convergence estimates for rate convergence. It shown that can improved employing special corrector. Other results are operator cell periodicity obtained Floquet–Bloch decomposition, two terms asymptotics band functions, complete asymptotic expansion bottom spectrum with an exponentially small error term.