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.

报告人简介：林萍，东北师范大学教授。主要研究领域为偏微分方程控制理论。在偏微分方程爆破点的反馈能控性以及具有爆破性质的偏微分方程的时间最优控制等问题上取得系列成果。已主持国家自然科学基金面上项目四项，在Journal de Mathematiques Pures et Appliques，SIAM J. Control Optim等杂志上发表论文多篇。