Some optimal control problems of multistate equations appearing in fluid mechanics

Frederic Abergel; Eduardo Casas

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1993)

  • Volume: 27, Issue: 2, page 223-247
  • ISSN: 0764-583X

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Abergel, Frederic, and Casas, Eduardo. "Some optimal control problems of multistate equations appearing in fluid mechanics." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 27.2 (1993): 223-247. <http://eudml.org/doc/193702>.

@article{Abergel1993,
author = {Abergel, Frederic, Casas, Eduardo},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {steady-state Navier-Stokes equations; well-posed linear elliptic system; optimality conditions},
language = {eng},
number = {2},
pages = {223-247},
publisher = {Dunod},
title = {Some optimal control problems of multistate equations appearing in fluid mechanics},
url = {http://eudml.org/doc/193702},
volume = {27},
year = {1993},
}

TY - JOUR
AU - Abergel, Frederic
AU - Casas, Eduardo
TI - Some optimal control problems of multistate equations appearing in fluid mechanics
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1993
PB - Dunod
VL - 27
IS - 2
SP - 223
EP - 247
LA - eng
KW - steady-state Navier-Stokes equations; well-posed linear elliptic system; optimality conditions
UR - http://eudml.org/doc/193702
ER -

References

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  1. [1] ABERGEL and R. TEMAM, 1990, On some control problems in fluid mechanics, Theoret. Comput. Fluid Dynamics, 1, 303-325. Zbl0708.76106
  2. [2] F. ABERGEL and R. TEMAM, 1992, Optimal control of turbulent flows, in Optimal control of viscous flows, S. S. Sritharan ed., Frontiers in Applied Mathematics Series, SIAM, Philadelphia. MR1632423
  3. [3] E. CASAS and L. FERNANDEZ, 1989, A Green's formula for quasilinear elliptic operators, J. of Math. Anal. & Appl., 142, 62-72. Zbl0704.35047MR1011409
  4. [4] H. CHOI, J. KIM, P. MOIN, R. TEMAM, à paraître, Methods of feedback controlfor distributed Systems and applications to Burgers equations. 
  5. [5] M. GAULTIER and M. LEZAUN, 1989, Equations de Navier-Stokes couplées à des équations de la chaleur : résolution par une méthode de point fixe endimension infinie, Ann. Sc. Math. Québec, 13, 1-17. Zbl0716.35064MR1006500
  6. [6] M. GUNZBURGER, L. Hou and T. SVOBODNY, 1991, Analysis and finite element approximations of optimal control problems for the stationary Navier-Stokes equations with Dirichlet conditions, M2AN, 25, 711-748. Zbl0737.76045MR1135991
  7. [7] M. GUNZBURGER, L. Hou and T. SVOBODNY, 1991, Boundary velocity controlof incompressible flow with an application to viscous drag reduction, SIAM J. on Control & Optimization. Zbl0756.49004
  8. [8] A. IOFFE and V. TIKHOMOROV, 1979, Extremal Problems, North-Holland, Amsterdam. 
  9. [9] J. LIONS, 1968, Contrôle de Systèmes Gouvernés pat des Equations aux Dérivées Partielles, Dunod, Paris. Zbl0179.41801
  10. [10] J. LIONS, 1969, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris. Zbl0189.40603
  11. [11] J. NEČAS, 1967, Les Méthodes Directes en Théorie des Equations Elliptiques, Editeurs Academia, Prague. MR227584
  12. [12] P. RABINOWITZ, 1968, Existence and nonuniqueness of rectangular solutions of the Benard problem, Arch Rational Mech. Anal., 29, 32-57. Zbl0164.28704MR233557
  13. [13] R. TEMAM, 1979, Navier-Stokes Equations, North-Holland, Amsterdam. Zbl0426.35003MR603444

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