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.
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},
     journal = {Applications of Mathematics},
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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. http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104098/

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