Advertisement

On the limit matrix obtained in the homogenization of an optimal control problem

  • S. Kesavan
  • M. Rajesh
Article

Abstract

A new formulation for the limit matrix occurring in the cost functional of an optimal control problem on homogenization is obtained. It is used to obtain an upper bound for this matrix (in the sense of positive definite matrices).

Keywords

Homogenization optimal control elliptic equations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Briane M, Damlamian A and Donato P, H-convergence for perforated domains, in: Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. XIII, Pitman Research Notes in Mathematics, 1996Google Scholar
  2. [2]
    Casado-Díaz J, Personal CommunicationGoogle Scholar
  3. [3]
    Kesavan S and Saint Jean Paulin J, Homogenization of an optimal control problem,SIAM J. Control Optim. 35 (1997) 1557–1573zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Kesavan S and Saint Jean Paulin J, Optimal control on perforated domains,J. Math. Anal. Appl. 229 (1999) 563–586zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Kesavan S and Vanninathan M, L’homogénéisation d’un probleme de contrôle optimal, C. R. Acad. Sci., Paris, Série A,285 (1977) 441–444zbMATHMathSciNetGoogle Scholar
  6. [6]
    Lions J L, Optimal Control of Systems Governed by Partial Differential Equations (Berlin: Springer-Verlag) (1971)zbMATHGoogle Scholar
  7. [7]
    Murat F, H-convergence, Mimeographed notes, Séminaire d’Analyse Fonctionnelle et Numérique, Université d’Alger, 1977/78Google Scholar
  8. [8]
    Murat F and Tartar L, H-convergence, in: Topics in the Mathematical Modelling of Composite Materials (eds) A Cherkaev and R Kohn (Birkhauser) (1997) 21–43Google Scholar
  9. [9]
    Rajesh M, Some Problems in Homogenization, Thesis (Indian Statistical Institute, Calcutta) (2000)Google Scholar
  10. [10]
    Tartar L, Compensated compactness and applications to partial differential equations, in: Nonlinear Analysis and Mechanics, Heriott Watt Symposium (ed) R J Knops, Pitman Research Notes in Mathematics,39 (1979) 136–212.MathSciNetGoogle Scholar

Copyright information

© Indian Academy of Sciences 2002

Authors and Affiliations

  • S. Kesavan
    • 2
    • 1
  • M. Rajesh
    • 2
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations