Remarks on non controllability of the heat equation with memory
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 288-300.

In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.

DOI : https://doi.org/10.1051/cocv/2012013
Classification : 93B
Mots clés : controllability, heat equation with memory
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     title = {Remarks on non controllability of the heat equation with memory},
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Guerrero, Sergio; Imanuvilov, Oleg Yurievich. Remarks on non controllability of the heat equation with memory. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 288-300. doi : 10.1051/cocv/2012013. http://www.numdam.org/articles/10.1051/cocv/2012013/

[1] A.V. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations, Seoul National University, Korea Lect. Notes. 34 (1996). | MR 1406566 | Zbl 0862.49004

[2] O.Yu. Imanuvilov, Controllability of parabolic equations (Russian) Mat. Sb. 186 (1995) 109-132; translation in Sb. Math. 186 (1995) 879-900. | MR 1349016 | Zbl 0845.35040

[3] S. Ivanov and L. Pandolfi, Heat equation with memory : Lack of controllability to rest. J. Math. Anal. Appl. 355 (2009) 1-11. | MR 2514446 | Zbl 1160.93008

[4] G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur (French). [Exact control of the heat equation]. Commun. Partial Differ. Equ. 20 (1995) 335-356. | MR 1312710 | Zbl 0819.35071

[5] J.-L. Lions, Exact controllability, stabilizability and perturbations for distributed systems. SIAM Rev. 30 (1988) 1-68. | MR 931277 | Zbl 0644.49028

[6] J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications I, Translated from the French by P. Kenneth, edited by Springer-Verlag, New York, Heidelberg. Die Grundlehren der Mathematischen Wissenschaften. 181 (1972). | MR 350177 | Zbl 0223.35039

[7] D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions. SIAM Rev. 20 (1978) 639-739. | MR 508380 | Zbl 0397.93001

[8] R. Temam, Navier-Stokes equations, Theory and numerical analysis, edited by North Holland Publishing Co., Amsterdam, New York, Oxford Studies in Math. Appl. 2 (1977). | MR 609732 | Zbl 0383.35057

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