偏微分方程式セミナー(2014/4/21): An example of Non-finite time stopping solution for 1-harmonic map flow equation, 黒田 紘敏氏 (北海道大学)

開催日時
2014年   4月 21日 17時 00分 ~ 2014年   4月 21日 18時 00分
場所
北海道大学理学部3号館3-309室
講演者
黒田 紘敏氏(北海道大学理学研究院LP推進室)
 
1-harmonic flow is the gradient system of the total variation in the L^2-topology. This system has a very strong diffusivity, so it is well-known that the solution tends to a steady solution in finite time under some boundary conditions.

In this talk we consider 1-harmonic 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.




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