  The main goal of this paper is to show that the blow up phenomenon (the
explosion of the $ \rL^{\infty }$-norm) of the solutions of several classes of
evolution problems can be controlled by means of suitable global controls
$\alpha (t)$ ($i.e.$ only dependent on time) in such a way that the
corresponding solution be well defined (as element of $\rL_{loc}^{1}(0,+\infty
:\rX)$, for some functional space $\rX$) after the explosion time. We start by
considering the case of an ordinary differential equation with a superlinear
term and show that the controlled explosion property holds by using a delayed
control (built through the solution of the problem and by generalizing the {\em
nonlinear variation of constants formula}, due to V.M. Alekseev in 1961, to the
case of {\em neutral delayed equations} (since the control is only in the space
$\rW_{loc}^{-1,q\prime }(0,+\infty :\RR )$, for some $q>1$)$.$ We apply those
arguments to the case of an evolution semilinear problem in which the
differential equation is a semilinear elliptic equation with a superlinear
absorption and the boundary condition is dynamic and involves the forcing
superlinear term giving rise to the blow up phenomenon. We prove that, under a
suitable balance between the forcing and the absorption terms, the blow up
takes place only on the boundary of the spatial domain which here is assumed to
be a ball $\rB_{\rR}$ and for a constant as initial datum.
