Regional null controllability of a linearized Crocco-type equation

SIAM Journal on Control and Optimization

Volumn 42, Issue 2, 2003, Pages 709-728

  Martinez, P ^a   Raymond, J P ^a   Vancostenoble, J ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Carleman estimates; Heat equation; Parabolic degenerate equation; Regional null controllability; Transport equation

Indexed keywords

CARLEMAN ESTIMATES; HEAT EQUATIONS; PARABOLIC DEGENERATE EQUATIONS; REGIONAL NULL CONTROLLABILITY; TRANSPORT EQUATIONS;

BOUNDARY CONDITIONS; BOUNDARY LAYERS; BOUNDARY VALUE PROBLEMS; DIFFUSION; INTEGRAL EQUATIONS; INTEGRATION; LAMINAR FLOW; MATHEMATICAL MODELS; PRANDTL NUMBER; PROBLEM SOLVING;

LINEAR EQUATIONS;

EID: 1942541489     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902403547     Document Type: Article

References (27)

1. B. AINSEBA AND S. ANITA, Local exact controllability of the age-dependent population dynamics with diffusion, Abstr. Appl. Anal., 6 (2001), pp. 357-368.
2. P. ALBANO AND P. CANNARSA, Lectures on Carleman Estimates for Elliptic and Parabolic Operators and Applications, in preparation.
3. S. ANITA AND V. BARBU, Null controllability of nonlinear connective heat equations, ESAIM Control Optim. Cale. Var., 5 (2000), pp. 157-173.
4. J.-M. BUCHOT, Stabilisation et contrôle optimal des équations de Prandtl, Ph.D. thesis, E.N.S.A.E. Toulouse, Toulouse, France, 2002.
5. J.-M. BUCHOT AND J.-P. RAYMOND, A linearized model for boundary layer equations, in Optimal Control of Complex Structures, Internat. Ser. Numer. Math. 139, Birkhäuser, Basel, 2002, pp. 31-42.
6. J.-M. BUCHOT AND P. VILLEDIEU, Construction de modéles pour le contrôle de la position de transition laminaire-turbulent sur une plaque plane, Technical report, 1/3754.00 DTIMT/T, 1999.
7. P. CANNARSA, P. MARTINEZ, AND J. VANCOSTENOBLE, Nulle contrôlabilité régionale pour des équations de la chaleur dégénérées, C. R. Mec. Acad. Sci. Paris, 330 (2002), pp. 397-401.
8. P. CANNARSA, P. MARTINEZ, AND J. VANCOSTENOBLE, Persistent Regional Null Controllability for a Class of Degenerate Parabolic Equations, in preparation.
9. S. DOLECKI AND D. L. RUSSELL, A general theory of observation and control, SIAM J. Control Optim., 15 (1977), pp. 185-220.
10. Y. V. EGOROV, Some problems in the theory of optimal control, Z. Vychisl. Mat. Mat. Fiz., 5 (1963), pp. 887-904.
11. C. FABRE, J. P. PUEL, AND E. ZUAZUA, Approximate controllability for the semilinear heat equation, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), pp. 31-61.
12. H. O. FATTORINI AND D. L. RUSSELL, Exact controllability theorems for linear parabolic equations in one space dimension, Arch. Ration. Mech. Anal. 4 (1971), pp. 272-292.
13. H. O. FATTORINI AND D. L. RUSSELL, Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations, Quart. Appl. Math., 32 (1974), p. 45-69.
14. E. FERNÁNDEZ-CARA AND E. ZUAZUA, The cost of approximate controllability for heat equations: The linear case, Adv. Differential Equations, 5 (2000), pp. 465-514.
15. E. FERNÁNDEZ-CARA AND E. ZUAZUA, Null and approximate controllability for weakly blowing-up semilinear heat equations, Ann. Inat. H. Poincaré Anal. Non Linéaire, 17 (2000), pp. 583-616.
16. A. V. FURSIKOV AND O. Y. IMANUVILOV, Controllability of Evolution Equations, Lecture Notes Ser. 34, Seoul National University, Seoul, Korea, 1996.
17. O. Yu. IMANUVILOV, Boundary controllability of parabolic equations, Mat. Sb., 186 (1995), pp. 109-132.
18. O. Yu. IMANUVILOV AND M. YAMAMOTO, On Carleman Inequalities for Parabolic Equations in Sobolev Spaces of Negative Order and Exact Controllability for Semilinear Parabolic Equations, preprint 98-46, University of Tokyo, Grade School of Mathematics, Komobo, Tokyo, Japan, 1998.
19. I. LASIECKA AND R. TRIGGIANI, Carleman estimates and exact boundary controllability for a system of coupled, non conservative second order hyperbolic equations, in Partial Differential Equations Methods in Control and Shape Analysis, Lecture Notes in Pure and Appl. Math. 188, Marcel Dekker, New York, 1994, pp. 215-243.
20. G. LEBEAU AND L. ROBBIANO, Contrôle exact de l'équation de la chaleur, Comm. Partial Differential Equations, 20 (1995), pp. 335-356.
21. J.-L. LIONS, Controle optimal des systemes gouvernes par des equations aux derivees partielles, Dunod, Paris, 1969.
22. P. MARTINEZ, J.-P. RAYMOND, AND J. VANCOSTENOBLE, Nulle contrôlabilité régionale d'une équation de type Crocco linéarisée, C. R. Math. Acad. Sci. Paris, 334 (2002), pp. 1-4.
23. O. A. OLEINIK AND V. N. SAMOKHIN, Mathematical Models in Boundary Layer Theory, Appl. Math. Math. Comput. 15, Chapman and Hall/CRC, Boca Raton, London, New York, 1999.
24. D. L. RUSSELL, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Stud. Appl. Math., 52 (1973), pp. 189-221.
25. D. TATARU, Carlemann estimates, unique continuation and controllability for anizotropic PDEs, in Optimization Methods in Partial Differential Equations, Contemp. Math. 209, 1997, pp. 267-279.
26. J. ZABCZYK, Mathematical Control Theory: An Introduction, Birkhauser Boston, Boston, 1992.
27. X. ZHANG, A remark on null exact controllability of the heat equation, SIAM J. Control Optim., 40 (2001), pp. 39-53.