Blowup rate of type II and the braid group theory


Prof. Noriko Mizoguchi  ( Tokyo Institute of Technology, Japan )

2008 - 01 - 16 (Wed.)
10:20 - 11:10
308, Mathematics Research Center Building (ori. New Math. Bldg.)

This talk is concerned with blowup rate of solutions to a Cauchy problem for a semilinear heat equation (1) It is well-known by Giga and Kohn that if p is subcritical in the Sobolev sense, then any solution of (1) fulfills (2) for with some constant C > 0. The blowup satisfying (2) is called of type I and of type II otherwise. In the supercritical case, the existence of type II blowup solutions was known. However, there has been no detailed information on the blowup rate of such solutions. I talk about the mechanism which determines the exact blowup rate of type II and the role of the braid group theory in the proof.