Asymptotic Analysis of an Optimal Control Problem Involving a Thick Two-Level Junction with Alternate Type of Controls

摘要

We study the asymptotic behavior (as epsilon -> 0) of an optimal control problem in a plane thick two-level junction, which is the union of some domain and a large number 2N of thin rods with variable thickness of order epsilon = O(N-1). The thin rods are divided into two levels depending on the geometrical characteristics and on the controls given on their bases. In addition, the thin rods from each level are epsilon-periodically alternated and the inhomogeneous perturbed Fourier boundary conditions are given on the lateral sides of the rods. Using the direct method of the calculus of variations and the Buttazzo-Dal Maso abstract scheme for variational convergence of constrained minimization problems, the asymptotic analysis of this problem for different kinds of controls is made as epsilon -> 0.