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arXiv · 2407.10521

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

Alessandro Duca·Eugenio Pozzoli·Cristina Urbani
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Abstract

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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Alessandro Duca, Eugenio Pozzoli, Cristina Urbani. 2024-07-15. On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories. https://arxiv.org/abs/2407.10521

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