Displaying similar documents to “Singular perturbation for the Dirichlet boundary control of elliptic problems”

Singular perturbation for the Dirichlet boundary control of elliptic problems

Faker Ben Belgacem, Henda El Fekih, Hejer Metoui (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for...

Penalization of Dirichlet optimal control problems

Eduardo Casas, Mariano Mateos, Jean-Pierre Raymond (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. The results are compared with some previous ones in the literature and are checked by a numerical experiment. A detailed study of the regularity of the solutions of the PDEs is carried out.

Sufficient optimality conditions for multivariable control problems

Andrzej Nowakowski (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.

Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method

S. S. Ravindran (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we study the boundary penalty method for optimal control of unsteady Navier–Stokes type system that has been proposed as an alternative for Dirichlet boundary control. Existence and uniqueness of solutions are demonstrated and existence of optimal control for a class of optimal control problems is established. The asymptotic behavior of solution, with respect to the penalty parameter , is studied. In particular, we prove convergence of solutions of penalized control problem...

Control-theoretic properties of structural acoustic models with thermal effects, II. Trace regularity results

Francesca Bucci (2008)

Applicationes Mathematicae

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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],...