Penalization of Dirichlet optimal control problems

Eduardo Casas; Mariano Mateos; Jean-Pierre Raymond

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 15, Issue: 4, page 782-809
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Casas, Eduardo, Mateos, Mariano, and Raymond, Jean-Pierre. "Penalization of Dirichlet optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 15.4 (2008): 782-809. <http://eudml.org/doc/90937>.

@article{Casas2008,
abstract = { 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. },
author = {Casas, Eduardo, Mateos, Mariano, Raymond, Jean-Pierre},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Dirichlet optimal control; Robin penalization; regularity of solutions},
language = {eng},
month = {8},
number = {4},
pages = {782-809},
publisher = {EDP Sciences},
title = {Penalization of Dirichlet optimal control problems},
url = {http://eudml.org/doc/90937},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Casas, Eduardo
AU - Mateos, Mariano
AU - Raymond, Jean-Pierre
TI - Penalization of Dirichlet optimal control problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/8//
PB - EDP Sciences
VL - 15
IS - 4
SP - 782
EP - 809
AB - 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.
LA - eng
KW - Dirichlet optimal control; Robin penalization; regularity of solutions
UR - http://eudml.org/doc/90937
ER -

References

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  1. J.-J. Alibert and J.-P. Raymond, Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls. Numer. Funct. Anal. Optim.18 (1997) 235–250.  Zbl0885.49010
  2. F. Ben Belgacem, H. El Fekih and H. Metoui, Singular perturbation for the Dirichlet boundary control of elliptic problems. ESAIM: M2AN37 (2003) 833–850.  Zbl1051.49012
  3. F. Ben Belgacem, H. El Fekih and J.-P. Raymond, A penalized Robin approach for solving a parabolic equation with nonsmooth Dirichlet boundary conditions. Asymptot. Anal.34 (2003) 121–136.  Zbl1043.35014
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  12. L.S. Hou and S.S. Ravindran, A penalized Neumann control approach for solving an optimal Dirichlet control problem for the Navier-Stokes equations. SIAM J. Contr. Opt.36 (1998) 1795–1814 (electronic).  Zbl0917.49003
  13. D. Jerison and C. Kenig, The Neumann problem on Lipschitz domains. Bull. Amer. Math. Soc. (N.S.)4 (1981) 203–207.  Zbl0471.35026
  14. D. Jerison and C.E. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal.130 (1995) 161–219.  Zbl0832.35034
  15. C.V. Pao, Nonlinear parabolic and elliptic equations. Plenum Press, New York (1992).  Zbl0777.35001
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  17. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble)15 (1965) 189–258.  Zbl0151.15401

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