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Abstract
We consider explosive solutions $y^{0}(t)$, $t\in \lbrack 0,T_{y^{0}}),$ of
some ordinary differential equations
\begin{equation*}
P(T_{y^{0}}):
\begin{array}{lc}
\frac{dy}{dt}(t)=f(y(t)),y(0)=y_{0}, &
\end{array}
\end{equation*}
where $f:$ $\mathbb{R}^{d}\rightarrow \mathbb{R}^{d}$ is a locally
Lipschitz superlinear function and $d\geq 1$. In this work we analyze the
following question of controlability: given $\epsilon >0$, a continuous
deformation $y(t)$ de $y^{0}(t)$, built as a solution of the perturbed
control problem obtained by replacing $f(y(t))$ by $f(y(t))+u(t),$ for a
suitable control $u$, such that $y(t)=y^{0}(t)$ for any $t\in \lbrack
0,T_{y^{0}}-\epsilon ]$ and such that $y(t)$ also blows up in $t=T_{y_{0}}$
but in such a way that $y(t)$ could be extended beyond $T_{y_{0}}$ as a
function $y\in L_{loc}^{1}(0,+\infty :\mathbb{R}^{d})$?
Mathematics Subject Classification: Primary: 35R10, 35R35; Secondary: 35K20.
\begin{equation} \\ \end{equation}
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