Asymptotics and Estimates of Degrees of Convergence in Three-Dimensional Boundary Value Problem with Frequent Interchange of Boundary Conditions

Abstract

We consider a singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent interchange of type of boundary condition on a lateral surface. These boundary conditions are prescribed by partition of lateral surface in a great number of narrow strips on those the Dirichlet and Neumann conditions are imposed by turns. We study the case of the homogenized problem containing Dirichlet condition on the lateral surface. When the width of strips varies slowly, we construct the leading terms of eigenelements' asymptotics expansions. We also estimate the degree of convergence for eigenvalues if the strips' width varies rapidly.