A Note on the Lack of Exact Controllability for Mild Solutions in Banach Spaces 论文

摘要

It is shown that exact controllability in finite time for linear control systems given on an infinite dimensional Banach space in integral form (mild solution) can never arise using locally $L_1 $-controls, if the associated $C_0 $ semigroup is compact for all $t > 0$. This includes, in particular, the class of parabolic partial differential equations defined on bounded spatial domains.