Abstract
In this chapter, we study a class of optimal control problems (OCPs) for a linear elliptic equation in a domain Ω ε ⊂ℝn (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)).
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References
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.
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.
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Kogut, P.I., Leugering, G.R. (2011). Asymptotic Analysis of Elliptic Optimal Control Problems in Thick Multistructures with Dirichlet and Neumann Boundary Controls. In: Optimal Control Problems for Partial Differential Equations on Reticulated Domains. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8149-4_13
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DOI: https://doi.org/10.1007/978-0-8176-8149-4_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-8148-7
Online ISBN: 978-0-8176-8149-4
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