Free Access
Issue
ESAIM: COCV
Volume 6, 2001
Page(s) 73 - 95
DOI https://doi.org/10.1051/cocv:2001104
Published online 15 August 2002
  1. N.U. Ahmed, Properties of relaxed trajectories for a class of nonlinear evolution equations on a Banach space. SIAM J. Control Optim. 21 (1983) 953-967. [CrossRef] [MathSciNet] [Google Scholar]
  2. N. Arada and J.P. Raymond, State-constrained relaxed control problems for semilinear elliptic equations. J. Math. Anal. Appl. 223 (1998) 248-271. [CrossRef] [MathSciNet] [Google Scholar]
  3. N. Arada and J.P. Raymond, Stability analysis of relaxed Dirichlet boundary control problems. Control Cybernet. 28 (1999) 35-51. [MathSciNet] [Google Scholar]
  4. J.M. Ball, A version of the fundamental theorem for Young's measures, in PDE's and Continuum Models of Phase Transition, edited by M. Rascle, D. Serre and M. Slemrod. Springer, Berlin, Lecture Notes in Phys. 344 (1989) 207-215. [CrossRef] [Google Scholar]
  5. E. Casas, The relaxation theory applied to optimal control problems of semilinear elliptic equations, in System Modelling and Optimization, edited by J. Dolezal and J. Fidler. Chapman & Hall, London (1996) 187-194. [Google Scholar]
  6. E. Di Benedetto, Degenerate Parabolic Equations. Springer-Verlag, New York (1993). [Google Scholar]
  7. R.J. DiPerna and A.J. Majda, Oscillation and concentrations in the weak solutions of the incompressible fluid equations. Comm. Math. Phys. 108 (1987) 667-689. [CrossRef] [MathSciNet] [Google Scholar]
  8. L.C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS 74. American Mathematical Society (1990). [Google Scholar]
  9. H.O. Fattorini, Infinite Dimensional Optimization and Control Theory, Encyclopedia of Mathematics and its Applications. Cambridge University Press (1998). [Google Scholar]
  10. R.V. Gamkrelidze, Principles of Optimal Control Theory. Plenum Press, New York (1978). [Google Scholar]
  11. A. Ghouila-Houri, Sur la généralisation de la notion de commande optimale d'un système guidable. Rev. Franç. Info. Rech. Oper. 1 (1967) 7-32. [Google Scholar]
  12. D. Kinderlehrer and P. Pedregal, Characterizations of Young measures generated by gradients. Arch. Rational Mech. Anal. 115 (1991) 329-365. [CrossRef] [MathSciNet] [Google Scholar]
  13. D. Kinderlehrer and P. Pedregal, Gradients Young measures generated by sequences in Sobolev spaces. J. Geom. Anal. 4 (1994) 59-90. [CrossRef] [MathSciNet] [Google Scholar]
  14. P.L. Lions, The concentration-compactness principle in the calculus of variations: The locally compact case, Parts. 1 and 2. Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 109-145, 223-283. [Google Scholar]
  15. E.J. McShane, Necessary conditions in the generalized-curve problems of the calculus of variations. Duke Math. J. 7 (1940) 513-536. [CrossRef] [Google Scholar]
  16. N.S. Papageorgiou, Properties of the relaxed trajectories of evolution equations and optimal control. SIAM J. Control Optim. 27 (1989) 267-288. [CrossRef] [MathSciNet] [Google Scholar]
  17. J.P. Raymond, Nonlinear boundary control of semilinear parabolic equations with pointwise state constraints. Discrete Contin. Dynam. Systems 3 (1997) 341-370. [CrossRef] [MathSciNet] [Google Scholar]
  18. J.P. Raymond and H. Zidani, Hamiltonian Pontryaguin's principles for control problems governed by semilinear parabolic equations. Appl. Math. Optim. 39 (1999) 143-177. [CrossRef] [MathSciNet] [Google Scholar]
  19. T. Roubícek, Relaxation in Optimization Theory and Variational Calculus. De Gruyter Series in Nonlinear Analysis and Applications (1997). [Google Scholar]
  20. T. Roubícek, Convex locally compact extensions of Lebesgue spaces anf their applications, in Calculus of Variations and Optimal Control, edited by A. Ioffe, S. Reich and I. Shafrir. Chapman & Hall, CRC Res. Notes in Math. 411, CRC Press, Boca Raton, FL (1999) 237-250. [Google Scholar]
  21. M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations. Comm. Partial Differential Equations 7 (1982) 959-1000. [CrossRef] [MathSciNet] [Google Scholar]
  22. L. Tartar, Compensated compactness and applications to partial differential equations. Nonlinear Analysis and Mechanics, Heriott-Watt Symposium IV, Pitmann Res. Notes in Math. 39 (1979). [Google Scholar]
  23. J. Warga, Optimal control of differential and functional equations. Academic Press, New York (1972). [Google Scholar]
  24. X. Xiang and N.U. Ahmed, Properties of relaxed trajectories of evolution equations and optimal control. SIAM J. Control Optim. 31 (1993) 1135-1142. [CrossRef] [MathSciNet] [Google Scholar]
  25. L.C. Young, Lectures on the Calculus of Variations and Optimal Control Theory. W.B. Saunders, Philadelphia (1969). [Google Scholar]

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