Feedback approximate controllability of blowup points for the heat equation with anti-interference blowup profile

This paper is concerned with a feedback approximate controllability problem of blowup points for the heat equation. We show that the system is approximately controllable for blowup points with feedback controls and the feedback operator is bounded at any time before blowup. It is also proved that the blowup profile for feedback controllability of blowup points is stable with respect to initial data. That is, suppose that the initial data has a very small perturbation, the blowup profiles also have tiny changes. More precisely, it just undergoes a tiny translation in space and time. This means that our feedback strategy is anti-interference.