| Title:
|
On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions (English) |
| Author:
|
Bock, Igor |
| Author:
|
Hlaváček, Ivan |
| Author:
|
Lovíšek, Ján |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
4 |
| Year:
|
1984 |
| Pages:
|
303-314 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented. (English) |
| Keyword:
|
nonlinear Kármán equations |
| Keyword:
|
transversal loading |
| Keyword:
|
Dirichlet boundary conditions |
| Keyword:
|
Existence of optimal control |
| Keyword:
|
differentiability |
| Keyword:
|
state function |
| MSC:
|
49A22 |
| MSC:
|
49J20 |
| MSC:
|
49K20 |
| MSC:
|
73K10 |
| MSC:
|
74G30 |
| MSC:
|
74H25 |
| MSC:
|
74K20 |
| MSC:
|
74P99 |
| idZBL:
|
Zbl 0554.73087 |
| idMR:
|
MR0754082 |
| DOI:
|
10.21136/AM.1984.104098 |
| . |
| Date available:
|
2008-05-20T18:25:26Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104098 |
| . |
| Reference:
|
[1] P. G. Ciarlet P. Rabier: Les équations de von Kármán.Springer Verlag, Berlin 1980. MR 0595326 |
| Reference:
|
[2] J. L. Lions: Sur le contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles.Dunod, Gauthier-Villars 1968. MR 0244606 |
| Reference:
|
[3] L. A. Ljusternik V. I. Sobolev: The elements of functional analysis.(in Russian). Moskva, Nauka 1965. MR 0209802 |
| Reference:
|
[4] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha 1967. MR 0227584 |
| . |
