Minimal time for the null controllability of parabolic systems:The effect of the condensation index of complex sequences

摘要

Let (A, D(A))be adiagonalizable generator of a C~0-semigroup of contractions on a complex Hilbert space X, B∈L(C, Y), Ybeing some suitable extrapolation space of X, and u ∈ L~2(0, T; C). Under some assumptions on the sequence of eigenvalues Λ ={λ_k}_k≥1?C of (A, D(A)), we prove the existence of a minimaltime T_0∈[0, ∞]depending on Bernstein's condensation index of Λand on Bsuch that y'=Ay+Buis null-controllable at any time T>T_0 and not null-controllable for T