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ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 58, Issue 1, pp 143–166 | Cite as

Asymptotic analysis and error estimates for an optimal control problem with oscillating boundaries

  • A. K. Nandakumaran
  • Ravi Prakash
  • J.-P. RaymondEmail author
Article

Abstract

In this article, we consider a distributed optimal control problem associated with the Laplacian in a domain with rapidly oscillating boundary. For simplicity, we consider a rectangular region in 2d with oscillations on one part of the boundary. We consider two types of functionals, namely a functional involving the L 2-norm of the state variable and another one involving its H 1-norm. The homogenization of the optimality system is obtained and then we derive appropriate error estimates in both cases.

Keywords

Optimal control and optimal solution Homogenization Oscillating boundary Interior control Adjoint system Error estimates 

Mathematics Subject Classification (2000)

35B27 35B40 35B37 49J20 49K20 

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Copyright information

© Università degli Studi di Ferrara 2011

Authors and Affiliations

  • A. K. Nandakumaran
    • 1
  • Ravi Prakash
    • 1
  • J.-P. Raymond
    • 2
    Email author
  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Institut de Mathématiques de ToulouseUniversité Paul Sabatier and CNRSToulouse CedexFrance

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