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Yoshitsugu Kabeya

2010-03-25
14:20:00 - 15:20:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

We consider the large time behavior of a solution to the Cauchy problem to a linear heat equation with a potential. We are interested in the relation between the behavior of the maximum points (hot spots) of the solution and the potential term. Without the potential term (usual heat equation), the behavior of the hot spots is investigated by Chavel and Karp and they showed that the hot spots converge to the center of mass of the compactly supported initial data. However, with a potential term, we will show that the hot spots goes to infinity or to the origin according to the sign of the potential as time goes by. This talk is based on the joint works with Kazuhiro Ishige of Tohoku University.