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Bock, Igor ; Hlaváček, Ivan ; Lovíšek, Ján
On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions. (English). Aplikace matematiky, vol. 29 (1984), issue 4, pp. 303-314
MSC: 49A22, 49J20, 49K20, 73K10, 74G30, 74H25, 74K20, 74P99 | MR 0754082 | Zbl 0554.73087 | DOI: 10.21136/AM.1984.104098
Keywords:
nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function
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.
Related articles:
On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions
On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load
References:
[1] P. G. Ciarlet P. Rabier: Les équations de von Kármán. Springer Verlag, Berlin 1980. MR 0595326
[2] J. L. Lions: Sur le contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles. Dunod, Gauthier-Villars 1968. MR 0244606
[3] L. A. Ljusternik V. I. Sobolev: The elements of functional analysis. (in Russian). Moskva, Nauka 1965. MR 0209802
[4] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Praha 1967. MR 0227584
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