Feedback controllability for blowup points of heat equation

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 $\hat{I}\text{c◯}$. 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 $\ddot{I}‰$ of this domain, such that the corresponding solution to this system blows up at time $T$ and holds unique point $a$. We show that $a\in \ddot{I}‰$ can be the unique blowup point of the corresponding solution with a certain feedback control, and for any feedback control, $a\in \hat{I}\text{c◯}\setminus \overline{\ddot{I}}‰$ could not be the unique blowup point.

40 pages