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Displaying 921 –
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We consider optimal control problems for convection-diffusion equations with a pointwise control
or a control localized on a smooth manifold. We prove optimality conditions for the control variable
and for the position of the control. We do not suppose that the coefficient of the convection term
is regular or bounded, we only suppose that it has the regularity of strong solutions of the
Navier–Stokes equations.
We consider functionals with an observation on the gradient of the state.
To obtain...
This paper deals with a nonlinear beam model which was published by D. Y. Gao in 1996. It is considered either pure bending or a unilateral contact with elastic foundation, where the normal compliance condition is employed. Under additional assumptions on data, higher regularity of solution is proved. It enables us to transform the problem into a control variational problem. For basic types of boundary conditions, suitable transformations of the problem are derived. The control variational problem...
Combining HUM and compactness arguments the exact controllability is prove for time dependent smooth kernels.
Dans ce papier, nous étudions un problème de contrôle par les coefficients issu de la lubrification élastohydrodynamique. La variable de contrôle est l’épaisseur du fluide. Le phénomène de cavitation est pris en compte par le modèle Elrod-Adams, connu pour ses performances dans la conservation des débits d’entrée et de sortie. L’idée est de régulariser dans l’équation d’état le graphe d’Heaviside, en l’approchant par une suite de fonctions monotones et régulières. Nous dérivons les conditions d’optimalité...
The purpose of this paper is to study a control by
coefficients problem issued from the elastohydrodynamic lubrication. The
control variable is the film thickness.The cavitation phenomenon takes place
and described by the Elrod-Adams model, suggested in preference to the
classical variational inequality due to its ability to describe input and
output flow.
The idea is to use the penalization in the state equation by
approximating the Heaviside graph whith a sequence of monotone and regular
functions....
We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data....
We consider a structural acoustic problem with the flexible wall modeled by a thermoelastic plate, subject to Dirichlet boundary control in the thermal component. We establish sharp regularity results for the traces of the thermal variable on the boundary in case the system is supplemented with clamped mechanical boundary conditions. These regularity estimates are most crucial for validity of the optimal control theory developed by Acquistapace et al. [Adv. Differential Equations, 2005], which ensures...
In this paper, we propose a new class of adaptive trust region methods for unconstrained optimization problems and develop some convergence properties. In the new algorithms, we use the current iterative information to define a suitable initial trust region radius at each iteration. The initial trust region radius is more reasonable in the sense that the trust region model and the
objective function are more consistent at the current iterate. The global convergence, super-linear and quadratic convergence...
In the article an optimal control problem subject to a stationary variational inequality is investigated. The optimal control problem is complemented with pointwise control constraints. The convergence of a smoothing scheme is analyzed. There, the variational inequality is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal control problem converge to solutions of the original one. Passing to the limit in the optimality system of the regularized problem...
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