Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2025

On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories

Résumé

In this work we analyse the small-time reachability properties of a nonlinear parabolic equation, by means of a bilinear control, posed on a torus of arbitrary dimension $d$. Under a saturation hypothesis on the control operators, we show the small-time approximate controllability between states sharing the same sign. Moreover, in the one-dimensional case $d=1$, we combine this property with a local exact controllability result, and prove the small-time exact controllability of any positive states towards the ground state of the evolution operator.

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Dates et versions

hal-04647802 , version 1 (15-07-2024)
hal-04647802 , version 2 (02-07-2025)

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Alessandro Duca, Eugenio Pozzoli, Cristina Urbani. On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories. Journal de Mathématiques Pures et Appliquées, 2025, 203, pp.103758. ⟨10.1016/j.matpur.2025.103758⟩. ⟨hal-04647802v2⟩
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