Geodesic
On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions
Applications of Mathematics, Tome 30 (1985) no. 5, pp. 375-392
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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.
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.
DOI : 10.21136/AM.1985.104164
Classification : 49A22, 49J20, 73C60, 74B99, 74H99, 74K20, 74P99
Keywords: system of von Kármán equations; thin elastic plate 
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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. Applications of Mathematics, Tome 30 (1985) no. 5, pp. 375-392. doi: 10.21136/AM.1985.104164

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[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

[3] P. G. Ciarlet P. Rabier: Les équations de von Kármán. Springer Verlag, Berlin 1980. | MR

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[5] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. | MR

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