THE EXISTENCE OF OPTIMAL SETS FOR LINEAR VARIATIONAL EQUATIONS AND INEQUALITIES

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详细

This paper considers an optimal control problem in which the controlled process is described by a linear functional equation in a Hilbert space, and the control action is a change of space. Sufficient conditions for the existence of a solution are obtained. The results are generalized to the case when the controlled process is described by a linear variational inequality.

作者简介

V. Zamuraev

Belarusian-Russian University

Email: vhz@tut.by
Mogilev, Belarus

参考

  1. Zamuraev, V.G., The existence of optimal spaces for linear functional equations, Differ. Equat., 2002, vol. 38, no. 7, pp. 1046–1049.
  2. Lions, J., The optimal control of distributed systems, Russ. Math. Surv., 1973, vol. 28, no. 4, pp. 13-46.
  3. Begis, D. Application de la m´ethode des ´el´ements finis `a l’approximation d’un probl`eme de domaine optimal. M´ethodes de r´esolution des probl`emes approch´es / D. Begis, R. Glowinski // Appl. Math. and Optim. — 1975. — V. 2, № 2. — P. 130–169.
  4. Chenais, D. On the existence of a solution in a domain identification problem / D. Chenais // J. Math. Anal. Appl. — 1975. — № 52. — P. 189–219.
  5. Hlav´aˇcek, I. Optimization of the domain in elliptic unilateral boundary value problems by finite element method / I. Hlav´aˇcek, J. Neˇcas // Analyse Num´erique. — 1982. — V. 16, № 4. — P. 351–373.
  6. Osipov, Yu.S. and Suetov, A.P., A problem of J.-L. Lions, Dokl. AN SSSR, 1984, vol. 276, no. 2, pp. 288–291.
  7. Pironneau, O. Optimal Shape Design for Elliptic Systems / O. Pironneau. — New York : SpringerVerlag, 1984. — 168 p.
  8. Haslinger, J. Introduction to Shape Optimization: Theory, Approximation, and Computation / J. Haslinger, R.A.E. M¨akinen. — Philadelphia : SIAM, 2003. — 273 p.
  9. Neittaanmaki, P. Optimization of Elliptic Systems: Theory and Applications / P. Neittaanmaki, J. Sprekels, D. Tiba. — New York : Springer, 2006. — 507 p.
  10. Burachik, R.S. Set-Valued Mappings and Enlargements of Monotone Operators / R.S. Burachik, A.N. Iusem. — New York : Springer, 2008. — 293 p.
  11. Mikhlin, S.G., Kurs matematicheskoy fiziki (Mathematical Physics Course), Moscow: Nauka, 1968.
  12. Brezis, H. Functional Analysis, Sobolev Spaces and Partial Differential Equations / H. Brezis. — New York : Springer, 2011. — 599 p.

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