# Null controllability of the semilinear heat equation

ESAIM: Control, Optimisation and Calculus of Variations (1997)

- Volume: 2, page 87-103
- ISSN: 1292-8119

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topFernández-Cara, E.. "Null controllability of the semilinear heat equation." ESAIM: Control, Optimisation and Calculus of Variations 2 (1997): 87-103. <http://eudml.org/doc/90516>.

@article{Fernández1997,

author = {Fernández-Cara, E.},

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

keywords = {controllability; semilinear heat equation; Schauder's fixed-point theorem},

language = {eng},

pages = {87-103},

publisher = {EDP Sciences},

title = {Null controllability of the semilinear heat equation},

url = {http://eudml.org/doc/90516},

volume = {2},

year = {1997},

}

TY - JOUR

AU - Fernández-Cara, E.

TI - Null controllability of the semilinear heat equation

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 1997

PB - EDP Sciences

VL - 2

SP - 87

EP - 103

LA - eng

KW - controllability; semilinear heat equation; Schauder's fixed-point theorem

UR - http://eudml.org/doc/90516

ER -

## References

top- [1] D. Chae, O.Yu. Imanuvilov and S.M. Kim: Exact controllability for semilinear parabolic equations with Neumann boundary conditions, to appear. Zbl0946.93007MR1420354
- [2] C. Fabre, J.P. Puel and E. Zuazua: Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinbourgh, 125 A, 1995, 31-61. Zbl0818.93032MR1318622
- [3] A.V. Fursikov and O.Yu. Imanuvilov: On controllability of certain Systems simulating a fluid flow, in Flow Control, IMA Vol. Math. Appl., 68, Ed. by M.D. Gunzburger, Springer-Verlag, New York, 1995. Zbl0922.93006MR1348646
- [4] A.V. Fursikov and O.Yu. Imanuvilov: Local exact controllability for 2-D Navier-Stokes equations, to appear.
- [5] O.Yu. Imanuvilov: Thesis, Moscow 1991(in russian);
- see also: Exact boundary controllability of the parabolic equation, Russian Math. Surveys, 48, No. 3, 1993, 211-212.
- [6] O.Yu. Imanuvilov: Boundary controllability of parabolic equations, Russian Acad. Sci. Sb. Math., 186, No. 6, 1995, 109-132. Zbl0845.35040MR1349016
- [7] O.A. Ladyzhenskaja, V.A. Solonnikov and N.N. Ural'ceva: Linear and quasilinear equations of parabolic type, Trans. Math. Monographs,Vol. 23, AMS, Providence, 1968. Zbl0174.15403
- [8] G. Lebeau and L. Robbiano: Contrôle exact de l'équation de la chaleur, Comm. P.D.E., 20, 1995, 335-356. Zbl0819.35071MR1312710
- [9] G. Lebeau and E. Zuazua: Null controllability of a system of linear thermoelasticity, Arch. Rat. Mech. Anal., to appear. Zbl1064.93501MR1620510
- [10] E. Zuazua: Exact boundary controllability for the semilinear wave equation, in Nonlinear differential equations and their applications, H. Brezis and J.L. Lions eds, Research Notes in Math. 10, Pitman, London, 1991, 357-391. Zbl0731.93011MR1131832
- [11] E. Zuazua: Exact controllability for semilinear wave equations in one space dimension, Ann. Inst. Henri Poincaré, Vol. 10, No. 1, 1993, 109-129. Zbl0769.93017MR1212631

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