On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions

We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions.

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On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load

Applications of Mathematics ◽

10.21136/am.1987.104262 ◽

1987 ◽

Vol 32 (4) ◽

pp. 315-331

Author(s):

Igor Bock ◽

Ivan Hlaváček ◽

Ján Lovíšek

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Von Karman ◽

Von Kármán

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Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2018023 ◽

2018 ◽

Vol 52 (3) ◽

pp. 1137-1172

Author(s):

Gouranga Mallik ◽

Neela Nataraj ◽

Jean-Pierre Raymond

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Error Estimates ◽

Numerical Approximation ◽

The State ◽

Distributed Optimal Control ◽

Von Karman ◽

Von Kármán Equations ◽

Von Kármán

In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Kármán equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed to discretize the state and adjoint variables. The control is discretized using piece-wise constant approximations. A priori error estimates are derived for the state, adjoint and control variables. Numerical results that justify the theoretical results are presented.

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BILINEAR OPTIMAL CONTROL OF THE VELOCITY TERM IN A VON KÁRMÁN PLATE EQUATION

The ANZIAM Journal ◽

10.1017/s1446181113000205 ◽

2013 ◽

Vol 54 (4) ◽

pp. 291-305

Author(s):

JONG YEOUL PARK ◽

SUN HYE PARK ◽

YONG HAN KANG

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Existence Of Solutions ◽

Plate Equation ◽

Spatial Variables ◽

Von Karman ◽

Von Kármán Plate ◽

Von Kármán ◽

Objective Functional

AbstractWe consider a bilinear optimal control problem for a von Kármán plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. We first state the existence of solutions for the von Kármán equation and then derive optimality conditions for a given objective functional. Finally, we show the uniqueness of the optimal control.

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Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

Asymptotic Analysis ◽

10.3233/asy-211685 ◽

2021 ◽

pp. 1-21

Author(s):

Claudia Gariboldi ◽

Takéo Takahashi

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Boundary Conditions ◽

Control Problem ◽

Stokes System ◽

Navier Stokes ◽

Slip Boundary Conditions ◽

Navier Slip ◽

Slip Boundary ◽

Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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