Free Access
Issue
ESAIM: COCV
Volume 17, Number 4, October-December 2011
Page(s) 975 - 994
DOI https://doi.org/10.1051/cocv/2010034
Published online 23 August 2010
  1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [Google Scholar]
  2. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures. North-Holland Company, Amsterdam (1978). [Google Scholar]
  3. C. Calvo-Jurado and J. Casado-Diaz, Homogenization of Dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design. J. Comput. Appl. Math. 192 (2006) 20–29. [CrossRef] [MathSciNet] [Google Scholar]
  4. J. Casado-Diaz, J. Couce-Calvo and J.D. Martin-Gómez, Optimality conditions for nonconvex multistate control problems in the coefficients. SIAM J. Control Optim. 43 (2004) 216–239. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Casas, Optimal Control in coefficients of elliptic equations with state constraints. Appl. Math. Optim. 26 (1992) 21–37. [CrossRef] [MathSciNet] [Google Scholar]
  6. I. Ciuperca, M. El Alaoui Talibi and M. Jai, On the optimal control of coefficients in elliptic problems, Application to the optimization of the head slider. ESAIM: COCV 11 (2005) 102–121. [CrossRef] [EDP Sciences] [Google Scholar]
  7. H. Gao and X. Li, Necessary conditions for optimal control of elliptic systems. J. Australian Math. Soc. Ser. B 41 (2000) 542–567. [CrossRef] [Google Scholar]
  8. A. Holmbom, Homogenization of parabolic equations an alternative approach and some corrector-type results. Appl. Math. 42 (1997) 321–343. [CrossRef] [MathSciNet] [Google Scholar]
  9. O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and Quasi-linear Equations of Parabolic Type, Transl. Math. Monographs 23. American Mathematical Society, Providence (1968). [Google Scholar]
  10. X. Li, and J. Yong, Optimal Control Theory for Infinite Dimensional Systems. Birkhäuser, Boston (1995). [Google Scholar]
  11. H. Lou and J. Yong, Optimality Conditions for Semilinear Elliptic Equations with Leading Term Containing Controls. SIAM J. Control Optim. 48 (2009) 2366–2387. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Murat and L. Tartar, Calculus of variations and homogenization, in Topics in the Mathematical Modelling of Composite Materials, Progress in Nonlinear Diffrential Equations and their Applications 31, L. Cherkaev and R.V. Kohn Eds., Birkaüser, Boston (1998) 139–174. [Google Scholar]
  13. U. Raitums and W.H. Schmidt, On necessary optimal conditions for optimal control problems governed by elliptic systems. Optimization 54 (2005) 149–160. [CrossRef] [MathSciNet] [Google Scholar]
  14. S.Y. Serovajsky, Sequential extension in the problem of control in coefficients for elliptic-type equations. J. Inverse Ill-Posed Probl. 11 (2003) 523–536. [CrossRef] [MathSciNet] [Google Scholar]
  15. R.K. Tagiyev, Optimal control by the coefficients of a parabolic equation. Trans. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. Math. Mech. 24 (2004) 247–256. [Google Scholar]
  16. L. Tartar, Estimations fines de coefficients homogénéisés, Ennio de Giorgi Colloquium, in Pitman Research Notes in Mathematics 125, P. Krée Ed., Pitman, London (1985) 168–187. [Google Scholar]

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