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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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).
|Uncontrolled Keywords:||Finite extinction time; Delayed feedback control; Linear parabolic equations|
|Subjects:||Sciences > Mathematics > Numerical analysis|
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|Deposited On:||03 May 2012 08:45|
|Last Modified:||06 Feb 2014 10:15|
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