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Bock, Igor ; Hlaváček, Ivan ; Lovíšek, Ján
On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions. (English). Aplikace matematiky, vol. 30 (1985), issue 5, pp. 375-392
MSC: 49A22, 49J20, 73C60, 74B99, 74H99, 74K20, 74P99 | MR 0806834 | Zbl 0614.73097 | DOI: 10.21136/AM.1985.104164
Keywords:
system of von Kármán equations; thin elastic plate
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.
Related articles:
On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet 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] M. S. Berger P. Fife: On Von Kármán equations and the buckling of a thin plate. Comm. Pure Appl. Math. 21 (1968), 227-241. DOI 10.1002/cpa.3160210303 | MR 0229978
[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
[3] P. G. Ciarlet P. Rabier: Les équations de von Kármán. Springer Verlag, Berlin 1980. MR 0595326
[4] I. Hlaváček J. Naumann: Inhomogeneous boundary value problems for the von Kármán equations I. Apl. Mat. 19 (1974), 253-269. MR 0377307
[5] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. MR 0227584
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