Díaz Díaz, Jesús IldefonsoCasal, A.C.Vegas Montaner, José Manuel2023-06-202023-06-202009-12-150362-546X10.1016/j.na.2009.03.008https://hdl.handle.net/20.500.14352/42156We 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).engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0362546X09004313http://www.sciencedirect.com/restricted access519.6Finite extinction timeDelayed feedback controlLinear parabolic equationsAnálisis numérico1206 Análisis Numérico