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.
Mots clés : controllability, heat equation with memory
@article{COCV_2013__19_1_288_0,
author = {Guerrero, Sergio and Imanuvilov, Oleg Yurievich},
title = {Remarks on non controllability of the heat equation with memory},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {288--300},
publisher = {EDP-Sciences},
volume = {19},
number = {1},
year = {2013},
doi = {10.1051/cocv/2012013},
mrnumber = {3023071},
zbl = {1258.93026},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2012013/}
}
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 SP - 288 EP - 300 VL - 19 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2012013/ DO - 10.1051/cocv/2012013 LA - en ID - COCV_2013__19_1_288_0 ER -
%0 Journal Article %A Guerrero, Sergio %A Imanuvilov, Oleg Yurievich %T Remarks on non controllability of the heat equation with memory %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 288-300 %V 19 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2012013/ %R 10.1051/cocv/2012013 %G en %F COCV_2013__19_1_288_0
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://archive.numdam.org/articles/10.1051/cocv/2012013/
[1] and , Controllability of Evolution Equations, Seoul National University, Korea Lect. Notes. 34 (1996). | MR | Zbl
[2] , Controllability of parabolic equations (Russian) Mat. Sb. 186 (1995) 109-132; translation in Sb. Math. 186 (1995) 879-900. | MR | Zbl
[3] and , Heat equation with memory : Lack of controllability to rest. J. Math. Anal. Appl. 355 (2009) 1-11. | MR | Zbl
[4] and , Contrôle exact de l'équation de la chaleur (French). [Exact control of the heat equation]. Commun. Partial Differ. Equ. 20 (1995) 335-356. | MR | Zbl
[5] , Exact controllability, stabilizability and perturbations for distributed systems. SIAM Rev. 30 (1988) 1-68. | MR | Zbl
[6] and , 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 | Zbl
[7] , Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions. SIAM Rev. 20 (1978) 639-739. | MR | Zbl
[8] , Navier-Stokes equations, Theory and numerical analysis, edited by North Holland Publishing Co., Amsterdam, New York, Oxford Studies in Math. Appl. 2 (1977). | MR | Zbl
Cité par Sources :
