%0 Journal Article
%A Díaz Díaz, Jesús Ildefonso
%A Casal, A.C.
%A Vegas Montaner, José Manuel
%T Finite extinction and null controllability via delayed feedback non-local actions
%D 2009
%@ 0362-546X
%U https://hdl.handle.net/20.500.14352/42156
%X 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).
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