Sharp estimates of the one-dimensional boundary control cost for parabolic systems
Manuel González-Burgos, Lydia Ouaili · Contemporary mathematics - American Mathematical Society · 2020
In this work we present new results on the cost of the boundary controllability of parabolic systems at time T > 0 T > 0 . In particular, we will study optimal estimates of the control cost at time T T ( T T small enough) when the eigenvalues of the generator of the C 0 C_0 semigroup accumulate and do not satisfy a gap condition. The main ingredient we will use is the moment method combined with sharp estimates of the L^2(0,T; \mathbb {C}\xspace ) -norm of the elements of biorthogonal families to complex exponentials.