Asymptotic Analysis of Elliptic Optimal Control Problems in Thick Multistructures with Dirichlet and Neumann Boundary Controls

Part of the Systems & Control: Foundations & Applications book series (SCFA)


In this chapter, we study a class of optimal control problems (OCPs) for a linear elliptic equation in a domain Ω ε ⊂ℝ n (thick multistructure), whose boundary Ω ε contains a very highly oscillating part with respect to ε, as ε→0. We consider this problem assuming that there are two types of the controls active via Neumann and Dirichlet boundary conditions posed on the different parts of the oscillating boundary (for a comparison, see Corbo Esposito, D’Apice, and Gaudiello (2002), De Maio, Gaudiello, and Lefter (2004)).


Weak Solution Optimal Control Problem Boundary Control Admissible Control Limit Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 73.
    A. Corbo Esposito, C. D’Apice, and A. Gaudiello. A homogenization problem in a perforated domain with both Dirichlet and Neumann conditions on the boundary of the holes. Asymp. Anal., 31:297–316, 2002. MathSciNetMATHGoogle Scholar
  2. 88.
    U. De Maio, A. Gaudiello, and C. Lefter. Optimal control for a parabolic problem in a domain with highly oscillating boundary. Applic. Anal., 83(12):1245–1264, 2004. MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and Mechanics, Department of Differential EquationsOles Honchar Dnipropetrovsk National UniversityDnipropetrovskUkraine
  2. 2.Department of Mathematics, Chair of Applied Mathematics IIFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

Personalised recommendations