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Finite extinction and null controllability via delayed feedback non-local actions

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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


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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
Uncontrolled Keywords:Finite extinction time; Delayed feedback control; Linear parabolic equations
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:15071
Deposited On:03 May 2012 08:45
Last Modified:12 Dec 2018 15:07

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