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

We give sufficient conditions to have the finite extinction for all solutions of linear parabolic reaction-diffusion equations of the type equation(1) View the MathML source∂u∂t−Δu=−M(t)u(t−τ,x) Turn MathJax on with a delay term τ>0τ>0, on ΩΩ, an open set of RN,M(t)RN,M(t) is a bounded linear map on Lp(Ω)Lp(Ω), u(t,x)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 ut−Δu=v(t,x)ut−Δu=v(t,x) by means of the delayed feedback term v(t,x)=−M(t)u(t−τ,x)v(t,x)=−M(t)u(t−τ,x).