PDE seminar: An example of Nonfinite time stopping solution for 1harmonic map flow equation
 Date

2014421 17:00 
2014421 18:00
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Hirotoshi Kuroda (Hokkaido University)

 1harmonic flow is the gradient system of the total variation in the L^2topology. This system has a very strong diffusivity, so it is wellknown that the solution tends to a steady solution in finite time under some boundary conditions.
In this talk we consider 1harmonic map flow with values in a unit sphere S^2 when initial data is a piecewise constant. Then there is a unique global solution under the Dirichlet condition in the class of piecewise constant functions. Moreover we construct a example of the solution which does not stop in finite time. This fact shows that there is a direction where the diffusion is not very strong for higher dimensional cases.