| Title:
|
Optimal design problems for a dynamic viscoelastic plate. I. Short memory material (English) |
| Author:
|
Bock, Igor |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
285-304 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with an optimal control problem with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequality. The existence and uniqueness theorem for the state problem and the existence of an optimal thickness function are proved. (English) |
| Keyword:
|
optimal control |
| Keyword:
|
viscoelastic plate |
| Keyword:
|
variable thickness |
| Keyword:
|
pseudohyperbolic variational inequality |
| Keyword:
|
penalization |
| MSC:
|
35L85 |
| MSC:
|
49J20 |
| MSC:
|
49J40 |
| MSC:
|
73F15 |
| MSC:
|
74Hxx |
| idZBL:
|
Zbl 0845.49001 |
| idMR:
|
MR1331919 |
| DOI:
|
10.21136/AM.1995.134295 |
| . |
| Date available:
|
2009-09-22T17:48:22Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134295 |
| . |
| Reference:
|
[1] V. Barbu, T. Precupanu: Convexity and optimization.Sitjhoff-Noordhoff, Amsterdam, 1978. |
| Reference:
|
[2] I. Bock, J. Lovíšek: Optimal control of a viscoelastic plate bending.Mathematische Nachrichten 125 (1986), 135–151. MR 0847355, 10.1002/mana.19861250109 |
| Reference:
|
[3] I. Bock, J. Lovíšek: An optimal control problem for a pseudoparabolic variational inequality.Applications of Mathematics 37 (1992), 62–80. MR 1152158 |
| Reference:
|
[4] H. Brézis: Problémes uniltéraux.Journal de Math. Pures et Appliqué 51 (1968), 1–168. |
| Reference:
|
[5] H. Brézis: Operateurs maximaux monotones et semigroupes.North Holland, Amsterdam, 1973. |
| Reference:
|
[6] J. Brilla: Linear viscoelastic plate bending analysis.Proc. XI-th Congress of Applied Mechanics, München, 1964. |
| Reference:
|
[7] H. Gajewski, K. Gröger, K. Zacharias: Nichlineare Operatorgleichungen und Operatordifferentialgleichungen.Akademie, Berlin, 1974. MR 0636412 |
| Reference:
|
[8] J. Nečas, I. Hlaváček: Mathematical theory of elastic and elastoplastic bodies.An introduction, Elsevier, Amsterdam, 1981. |
| Reference:
|
[9] O.R. Ržanicyn: Teoria polzučesti.Strojizdat, Moskva, 1968. |
| Reference:
|
[10] D. Tiba: Some remarks on the control of the vibrating string with an obstacle.Revue Roumaine de Math. Pures, Appl. 29 (1984), 899–906. MR 0780134 |
| Reference:
|
[11] D. Tiba: Optimal control of nonsmooth distributed parameter systems.Springer-Verlag, Berlin, 1990. Zbl 0732.49002, MR 1090951 |
| . |
