# Null controllability of nonlinear convective heat equations

ESAIM: Control, Optimisation and Calculus of Variations (2000)

- Volume: 5, page 157-173
- ISSN: 1292-8119

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topAnita, Sebastian, and Barbu, Viorel. "Null controllability of nonlinear convective heat equations." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 157-173. <http://eudml.org/doc/90564>.

@article{Anita2000,

author = {Anita, Sebastian, Barbu, Viorel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Carleman estimates; interpolation inequality; Kakutani fixed point theorem; nonlinear partial differential equation; exact null controllability},

language = {eng},

pages = {157-173},

publisher = {EDP Sciences},

title = {Null controllability of nonlinear convective heat equations},

url = {http://eudml.org/doc/90564},

volume = {5},

year = {2000},

}

TY - JOUR

AU - Anita, Sebastian

AU - Barbu, Viorel

TI - Null controllability of nonlinear convective heat equations

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2000

PB - EDP Sciences

VL - 5

SP - 157

EP - 173

LA - eng

KW - Carleman estimates; interpolation inequality; Kakutani fixed point theorem; nonlinear partial differential equation; exact null controllability

UR - http://eudml.org/doc/90564

ER -

## References

top- [1] R.A. Adams, Sobolev Spaces. Academic Press, New York ( 1975). Zbl0314.46030MR450957
- [2] V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic Press, Boston ( 1993). Zbl0776.49005MR1195128
- [3] V. Barbu, Exact controllability of the superlinear heat equation. Appl. Math. Optim., to appear. Zbl0964.93046MR1751309
- [4] V. Barbu, T. Precupanu, Convexity and Optimization in Banach Spaces. D. Reidel Publ. Company, Dordrecht ( 1986). Zbl0594.49001MR860772
- [5] H. Brézis and A. Friedman, Nonlinear parabolic equations involving measures as initial conditions. J. Math. Pures Appl. 62 ( 1983) 73-97. Zbl0527.35043MR700049
- [6] K. Deimling, Nonlinear Functional Analysis. Springer-Verlag, Berlin ( 1985). Zbl0559.47040MR787404
- [7] C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation, Proceedings Royal Soc. Edinburgh 125 A ( 1995) 31-61. Zbl0818.93032MR1318622
- [8] E. Fernández-Cara, Null controllability of the semilinear heat equation. ESAIM Control. Optim. Calc. Var. 2 ( 1997) 87-107. Zbl0897.93011MR1445385
- [9] E. Fernández-Cara and E. Zuazua, The cost of approximate controllability for heat equations: The linear case. Adv. Diff. Equations, to appear. Zbl1007.93034MR1750109
- [10] E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. Zbl0970.93023MR1791879
- [11] A.V. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations. RIM Seoul National University, Korea, Lecture Notes Ser. 34 ( 1996). Zbl0862.49004MR1406566
- [12] 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). Zbl1065.35079MR1987865
- [13] O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Uraltzeva, Linear and Quasilinear Equations of Paraboic Type. Nauka, Moskow ( 1967). Zbl0164.12302
- [14] G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur. Comm. Partial Differential Equations 30 ( 1995) 335-357. Zbl0819.35071MR1312710
- [15] J.L. Lions, Controle des systèmes distribués singuliers, MMI 13. Gauthier-Villars ( 1983). Zbl0514.93001MR712486
- [16] J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris ( 1968). Zbl0165.10801MR247243
- [17] E. Zuazua, Approximate controllability of the semilinear heat équation: boundary control, in Computational Sciences for the 21st Century, M.O. Bristeau et al, Eds. John Wiley & Sons ( 1997) 738-747. Zbl0916.93016
- [18] E. Zuazua, Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities. Control Cybernet., to appear. Zbl0959.93025MR1782020

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