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This paper studies a controllability problem for blowup points of two classes of semilinear heat equations.Our goal to act controls on the systems we studied is to make the corresponding solutions blow upat given points. This differs with the controllability problem of equations with the property of blowup in the references, where the purpose of using controls is to prevent blowupby controls. We obtain the feedback controls for our controllability problem of blowup points.

This paper is concerned with some optimal control problems for equations with blowup or quenching property. We first study the existence and Pontryagin's maximum principle for optimal controls which have the minimal energy among all the controls whose corresponding solutions blow up at the right-hand time end-point of a given functional. Then, the same problem for quenching case is discussed. Finally, we establish Pontryagin's maximum principle for optimal controls of extended problems after quenching.

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