### Impacto

Díaz Díaz, Jesús Ildefonso and Casal, A.C. and Vegas Montaner, José Manuel
(2009)
*Finite extinction and null controllability via delayed feedback non-local actions.*
Nonlinear analysis-theory methods & applications, 71
(12).
pp. 2018-2022.
ISSN 0362-546X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X09004313

## Abstract

We give sufficient conditions to have the finite extinction for all solutions of linear parabolic reaction-diffusion equations of the type partial derivative u/partial derivative t - Lambda u = -M(t)u(t - tau, x) (1) with a delay term tau > 0, on Omega, an open set of R(N), M(t) is a bounded linear map on L(p)(Omega), u(t, x) satisfies a homogeneous Neumann or Dirichlet boundary condition. We apply this result to obtain distributed null controllability of the linear heat equation u(t) - Delta u = upsilon(t, x) by means of the delayed feedback term upsilon(t, x) = -M(t)u(t - tau, x).

Item Type: | Article |
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Uncontrolled Keywords: | Finite extinction time; Delayed feedback control; Linear parabolic equations |

Subjects: | Sciences > Mathematics > Numerical analysis |

ID Code: | 15071 |

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Deposited On: | 03 May 2012 08:45 |

Last Modified: | 06 Feb 2014 10:15 |

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