# Remarks on non controllability of the heat equation with memory

Sergio Guerrero; Oleg Yurievich Imanuvilov

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 1, page 288-300
- ISSN: 1292-8119

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topGuerrero, Sergio, and Imanuvilov, Oleg Yurievich. "Remarks on non controllability of the heat equation with memory." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 288-300. <http://eudml.org/doc/272784>.

@article{Guerrero2013,

abstract = {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.},

author = {Guerrero, Sergio, Imanuvilov, Oleg Yurievich},

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

keywords = {controllability; heat equation with memory},

language = {eng},

number = {1},

pages = {288-300},

publisher = {EDP-Sciences},

title = {Remarks on non controllability of the heat equation with memory},

url = {http://eudml.org/doc/272784},

volume = {19},

year = {2013},

}

TY - JOUR

AU - Guerrero, Sergio

AU - Imanuvilov, Oleg Yurievich

TI - Remarks on non controllability of the heat equation with memory

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2013

PB - EDP-Sciences

VL - 19

IS - 1

SP - 288

EP - 300

AB - 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.

LA - eng

KW - controllability; heat equation with memory

UR - http://eudml.org/doc/272784

ER -

## References

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- [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). Zbl0223.35039MR350177
- [7] D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions. SIAM Rev. 20 (1978) 639–739. Zbl0397.93001MR508380
- [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). Zbl0383.35057MR609732

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