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.
Keywords: 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},
year = {2013},
publisher = {EDP Sciences},
volume = {19},
number = {1},
doi = {10.1051/cocv/2012013},
mrnumber = {3023071},
zbl = {1258.93026},
language = {en},
url = {https://www.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 - https://www.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 https://www.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
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