In this talk, we consider 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.

Speaker Profile: Lin Ping, a professor at Northeast Normal University. The main research field is the control theory of partial differential equations. A series of achievements have been made in issues such as the feedback controllability of the burst point of partial differential equations and the time optimal control of partial differential equations with burst properties. He/She has presided over four general projects of the National Natural Science Foundation of China and published many papers in journals such as Journal de Mathematiques Pures et Appliques and SIAM J. Control Optim.