Optimal shape control problem for the Navier-Stokes equations, part 2

Journal of Optimization Theory and Applications

Volumn 118, Issue 1, 2003, Pages 135-156

  Ton, B A ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Closed loop multicontrol problems; Feedback laws; Inverse problems; Navier Stokes equations; Shape design

Indexed keywords

FEEDBACK CONTROL; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; VISCOUS FLOW;

A-PLANE; CLOSED-LOOP; CLOSED-LOOP MULTICONTROL PROBLEM; CONTROL PROBLEMS; FEEDBACK LAWS; MEASUREMENTS OF; NAVIER-STOKES EQUATION; NONSTATIONARY INCOMPRESSIBLE FLOWS; OPTIMAL SHAPE CONTROL; SHAPE DESIGNS;

INVERSE PROBLEMS;

EID: 0037829555     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024743609511     Document Type: Article

References (15)

1. PIRONNEAU, O., Optimal Design in Fluid Mechanics, Journal of Fluid Mechanics, Vol. 64, pp. 97-110, 1974.
2. GUNZBURGER, M., and KIM, H., Existence of an Optimal Solution of a Shape Control Problem for the Stationary Navier-Stokes Equations, SIAM Journal on Control and Optimization, Vol. 36, pp. 895-909, 1998.
3. TON, B. A., Optimal Shape Control Problem for the Navier-Stokes Equations, SIAM Journal on Control and Optimization (to appear).
4. HE, J. W., GLOWINSKI, R., METCALFE, R., NORDLANDER, A., and PERIAUX, J., Active Control and Drag Reduction for Flow Past a Circular Cylinder, I: Oscillatory Cylinder Rotation, Journal of Computational Physics, Vol. 163, pp. 83-117, 2000.
5. HE, J. W., GLOWINSKI, R., METCALFE, R., NORDLANDER, A., and PERIAUX, J., Drag Reduction by Active Control for Flow Past Cylinders, Computational Mathematics Driven by Industry, Edited by V. Cappaso, H. Engl, J. Periaux, Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, Vol. 1734, pp. 287-363, 2000.
6. CEA, J., Problems of Shape Optimal Design, Optimization of Distributed-Parameters Structures, Edited by J. Cea and E. J. Haug, Sijthoff and Noordhoff, Alphen aan den Rijn, Netherlands, pp. 1049-1988, 1981.
7. CHAVENT, J., On Parameter Identifiability, Proceedings of the 7th IFAC Symposium on Identification and Systems Parameter Estimation, Pergamon Press, New York, NY, pp. 531-536, 1985.
8. JAMES, F., and SEPULDEVA, M., Parameter Identification for a Model of Chromatographic Column, Inverse Problems, Vol. 10, pp. 367-385, 1994.
9. KIM, H., Penalized Approach and Analysis of an Optimal Shape Control Problem for the Stationary Navier-Stokes Equations, Journal of the Korean Mathematical Society, Vol. 38, pp. 1-23, 2001.
10. LENHART, S., PROTOPOPESCU, V., and YONG, J., Identification of Boundary Shape and Reflectivity in a Wave Equation by Optimal Control Techniques, Differential and Integral Equations, Vol. 13, pp. 941-972, 2000.
11. LENHART, S, PROTOPOPESCU, V., and YONG, J., Solving Inverse Problems of Identification by Optimal Control Techniques, Proceedings of the International Conference on Advances of Nonlinear Dynamics Near the Millenium, pp. 87-94, 1997.
12. POPA, C., Feedback Laws for Nonlinear Distributed Control Problems via Trotter-Type Formulae, SIAM Journal on Control and Optimization, Vol. 33, pp. 971-999, 1995.
13. LIONS, J. L., Quelques Methodes de Resolution des Problèmes aux Limites non Lineaires, Dunod, Paris, France, 1969.
14. TEMAM, R., Navier-Stokes Equations, North Holland, Amsterdam, Holland, 1979.
15. TON, B. A., Closed-Loop Control for Evolution Inclusions, Numerical Functional Analysis and Optimization, Vol. 20, pp. 983-1001, 1999.