Controllability of parabolic equations

This paper studies two problems of exact controllability of semilinear parabolic equations. In the first, the control is on the right-hand side of the parabolic equation and distributed over an arbitrary subdomain $\omega$ of the domain $\Omega$. In the second, the control is contained in the boundary conditions and distributed over a subdomain $\Gamma_0$ of the boundary $\partial\Omega$. If the original data satisfy certain conditions, then both problems are solvable.