| Title:
|
On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions (English) |
| Author:
|
Bock, Igor |
| Author:
|
Hlaváček, Ivan |
| Author:
|
Lovíšek, Ján |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
30 |
| Issue:
|
5 |
| Year:
|
1985 |
| Pages:
|
375-392 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A control of the system of Kármán's equations for a thin elastic plate is considered. Existence of an optimal transversal load and optimal stress function, respectively, is proven. The set of admissible functions is chosen in a way guaranteeing the unique solvability of the state problem. The differentiability of the state function with respect to the control variable, uniqueness of the optimal control and some necessary conditions of optimality are discussed. (English) |
| Keyword:
|
system of von Kármán equations |
| Keyword:
|
thin elastic plate |
| MSC:
|
49A22 |
| MSC:
|
49J20 |
| MSC:
|
73C60 |
| MSC:
|
74B99 |
| MSC:
|
74H99 |
| MSC:
|
74K20 |
| MSC:
|
74P99 |
| idZBL:
|
Zbl 0614.73097 |
| idMR:
|
MR0806834 |
| DOI:
|
10.21136/AM.1985.104164 |
| . |
| Date available:
|
2008-05-20T18:28:25Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104164 |
| . |
| Reference:
|
[1] M. S. Berger P. Fife: On Von Kármán equations and the buckling of a thin plate.Comm. Pure Appl. Math. 21 (1968), 227-241. MR 0229978, 10.1002/cpa.3160210303 |
| Reference:
|
[2] I. Bock I. Hlaváček J. Lovíšek: On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions.Apl. Mat. 29, (1984), 303-314. MR 0754082 |
| Reference:
|
[3] P. G. Ciarlet P. Rabier: Les équations de von Kármán.Springer Verlag, Berlin 1980. MR 0595326 |
| Reference:
|
[4] I. Hlaváček J. Naumann: Inhomogeneous boundary value problems for the von Kármán equations I.Apl. Mat. 19 (1974), 253-269. MR 0377307 |
| Reference:
|
[5] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| . |
