| Title:
|
An optimal control problem for a pseudoparabolic variational inequality (English) |
| Author:
|
Bock, Igor |
| Author:
|
Lovíšek, Ján |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
62-80 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with an optimal control problem governed by a pseudoparabolic variational inequality with controls in coefficients and in convex sets of admissible states. The existence theorem for an optimal control parameter will be proved. We apply the theory to the original design problem for a deffection of a viscoelastic plate with an obstacle, where the variable thickness of the plate appears as a control variable. (English) |
| Keyword:
|
optimal control |
| Keyword:
|
pseudoparabolic variational inequality |
| Keyword:
|
convex set |
| Keyword:
|
penalization |
| Keyword:
|
viscoelastic plate |
| Keyword:
|
thickness |
| Keyword:
|
obstacle |
| Keyword:
|
elliptic operators |
| MSC:
|
47H19 |
| MSC:
|
49A29 |
| MSC:
|
49A34 |
| MSC:
|
49J40 |
| MSC:
|
73F15 |
| MSC:
|
73K10 |
| MSC:
|
73V25 |
| MSC:
|
73k40 |
| MSC:
|
74Hxx |
| idZBL:
|
Zbl 0772.49008 |
| idMR:
|
MR1152158 |
| DOI:
|
10.21136/AM.1992.104492 |
| . |
| Date available:
|
2008-05-20T18:43:06Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104492 |
| . |
| Reference:
|
[1] V. Barbu: Optimal control of variational inequalities.Pitman, Boston, 1984. Zbl 0574.49005, MR 0742624 |
| Reference:
|
[2] V. Barbu T. Precupanu: Convexity and optimization.Sitjhoff-Noordhoff, Amsterdam, 1978. |
| Reference:
|
[3] I. Bock J. Lovíšek: Optimal control of a viscoelastic plate bending.Mathematische Nachrichten 125 (1968), 135-151. MR 0847355, 10.1002/mana.19861250109 |
| Reference:
|
[4] I. Bock J. Lovíšek: Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints.Aplikace matematiky 32 no. 4 (1987), 301-314. MR 0897834 |
| Reference:
|
[5] H. Brézis: Problémes unilatéraux.Journal de Math. Pures. et Appl. 51 (1972), 1-168. MR 0428137 |
| Reference:
|
[6] H. Brézis: Operateurs maximaux monotones et semigroupes.North Holland, Amsterdam, 1973. |
| Reference:
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[7] H. Brézis: Analyse fonctionelle.Masson, Paris, 1982. |
| Reference:
|
[8] J. Brilla: Linear viscoelastic plate bending analysis.Proc. XI-th Congress of applied mechanics, München, 1964. |
| Reference:
|
[9] E. Di Benedetto R.E.Showalter: A pseudoparabolic variational inequality and Stefan problem.Nonlinear analysis 6 (1982), 279-291. MR 0654319, 10.1016/0362-546X(82)90095-5 |
| Reference:
|
[10] H. Gajewski K. Gröner K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademie, Berlin, 1974. MR 0636412 |
| Reference:
|
[11] D. Kinderlehrer G. Stampacchia: An introduction to variational inequalities.Academic Press, New York, 1980. MR 0567696 |
| Reference:
|
[12] K. L. Kuttler, Jr.: Degenerate variational inequalities of evolution.Nonlinear analysis 8 (1984), 837-850. Zbl 0549.49004, MR 0753762, 10.1016/0362-546X(84)90106-8 |
| Reference:
|
[13] J. L. Lions: Quelques méthodes de résolution des problémes aux limites non linéaires.Dunod, Paris, 1969. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[14] U. Mosco: Convergence of convex sets of solutions of variational inequalities.Advances of Math. 3 (1969), 510-585. MR 0298508, 10.1016/0001-8708(69)90009-7 |
| Reference:
|
[15] O. R. Ržanicyn: Teoria polzučesti.Strojizdat, Moskva, 1968. |
| Reference:
|
[16] L. W. White: Control problems governed by pseudoparabolic partial differential equations.Trans. Amer. Math. Soc. 250 (1979), 235-246. MR 0530053, 10.1090/S0002-9947-1979-0530053-5 |
| Reference:
|
[17] L. W. White: Controlability properties of pseudoparabolic boundary value problems.SIAM J. of Control and Optim. 18 no. 5 (1980), 534-539. MR 0586169, 10.1137/0318039 |
| . |
