Geodesic
On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions
Applications of Mathematics, Tome 29 (1984) no. 4, pp. 303-314
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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.
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.
DOI : 10.21136/AM.1984.104098
Classification : 49A22, 49J20, 49K20, 73K10, 74G30, 74H25, 74K20, 74P99
Keywords: nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function 
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     title = {On the optimal control problem governed by the equations of von {K\'arm\'an.} {I.} {The} homogeneous {Dirichlet} boundary conditions},
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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. Applications of Mathematics, Tome 29 (1984) no. 4, pp. 303-314. doi: 10.21136/AM.1984.104098

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[2] J. L. Lions: Sur le contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles. Dunod, Gauthier-Villars 1968. | MR

[3] L. A. Ljusternik V. I. Sobolev: The elements of functional analysis. (in Russian). Moskva, Nauka 1965. | MR

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

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