Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015
We consider explosive solutions y 0 (t), t ∈ [0, T y 0), of some ordinary differential equations ... more We consider explosive solutions y 0 (t), t ∈ [0, T y 0), of some ordinary differential equations P (T y 0) : dy dt (t) = f (y(t)), y(0) = y 0 , where f : R d → R d is a locally Lipschitz superlinear function and d ≥ 1. In this work we analyze the following question of controlability: given > 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 ∈ [0, T y 0 − ] and such that y(t) also blows up in t = Ty 0 but in such a way that y(t) could be extended beyond Ty 0 as a function y ∈ L 1 loc (0, +∞ : R d)?
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