On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions

Igor Bock; Ivan Hlaváček; Ján Lovíšek

Aplikace matematiky (1985)

  • Volume: 30, Issue: 5, page 375-392
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Bock, Igor, Hlaváček, Ivan, and Lovíšek, Ján. "On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions." Aplikace matematiky 30.5 (1985): 375-392. <http://eudml.org/doc/15418>.

@article{Bock1985,
abstract = {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.},
author = {Bock, Igor, Hlaváček, Ivan, Lovíšek, Ján},
journal = {Aplikace matematiky},
keywords = {system of von Kármán equations; thin elastic plate; system of von Kármán equations; thin elastic plate},
language = {eng},
number = {5},
pages = {375-392},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions},
url = {http://eudml.org/doc/15418},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Bock, Igor
AU - Hlaváček, Ivan
AU - Lovíšek, Ján
TI - On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 5
SP - 375
EP - 392
AB - 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.
LA - eng
KW - system of von Kármán equations; thin elastic plate; system of von Kármán equations; thin elastic plate
UR - http://eudml.org/doc/15418
ER -

References

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  1. M. S. Berger P. Fife, 10.1002/cpa.3160210303, Comm. Pure Appl. Math. 21 (1968), 227-241. (1968) MR0229978DOI10.1002/cpa.3160210303
  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. (1984) MR0754082
  3. P. G. Ciarlet P. Rabier, Les équations de von Kármán, Springer Verlag, Berlin 1980. (1980) MR0595326
  4. I. Hlaváček J. Naumann, Inhomogeneous boundary value problems for the von Kármán equations I, Apl. Mat. 19 (1974), 253-269. (1974) MR0377307
  5. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584

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