PARTIAL CONTROLLABILITY OF SEMILINEAR SYSTEMS

The paper considers semilinear control system in the product of Hilbert spaces $X=H\times G$ driven by densely defined closed linear operator $A$ generating a strongly continuous semigroup. For the linear operator $L$, projecting $X$ to $H$, it is proved a sufficient condition for $L$-partially exact controllability to $L(D(A))$ which means that for every initial state $\xi \in X$ and every $\eta \in D(A)$ there exists a control $u$ such that $Lx^{\xi ,u}(T)=L\eta $, where $x^{\xi ,u}$ is the state process corresponding the initial state $\xi $ and the control $u$. The result is demonstrated on examples.