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

Abstract

top
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.

How to cite

top

Guerrero, 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

top
  1. [1] A.V. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations, Seoul National University, Korea Lect. Notes. 34 (1996). Zbl0862.49004MR1406566
  2. [2] O.Yu. Imanuvilov, Controllability of parabolic equations (Russian) Mat. Sb. 186 (1995) 109–132; translation in Sb. Math. 186 (1995) 879–900. Zbl0845.35040MR1349016
  3. [3] S. Ivanov and L. Pandolfi, Heat equation with memory : Lack of controllability to rest. J. Math. Anal. Appl.355 (2009) 1–11. Zbl1160.93008MR2514446
  4. [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. Zbl0819.35071MR1312710
  5. [5] J.-L. Lions, Exact controllability, stabilizability and perturbations for distributed systems. SIAM Rev.30 (1988) 1–68. Zbl0644.49028MR931277
  6. [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. [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. [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

NotesEmbed ?

top

You must be logged in to post comments.