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arXiv · 2107.02436

Feedback controllability for blowup points of heat equation

Ping Lin·Hatem Zaag
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Abstract

This paper concerns a controllability problem for blowup points on heat equation. It can be described as follows: In the absence of control, the solution to the linear heat system globally exists in a bounded domain $\Omega$. While, for a given time $T>0$ and a point $a$ in this domain, we find a feedback control, which is acted on an internal subset $\omega$ of this domain, such that the corresponding solution to this system blows up at time $T$ and holds unique point $a$. We show that $a\in \omega$ can be the unique blowup point of the corresponding solution with a certain feedback control, and for any feedback control, $a\in \Omega\setminus \overline{\omega}$ could not be the unique blowup point.

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Ping Lin, Hatem Zaag. 2021-07-06. Feedback controllability for blowup points of heat equation. https://arxiv.org/abs/2107.02436

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