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Ken Shirakawa

2011-08-30
09:30:00 - 10:20:00

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

This study is based on the jointwork with Prof. H. Watanabe, Salesian Polytechnic, Japan.

In this talk, a coupled system of two parabolic type equation is considered. The presented system is a one-dimensional version of a phase field model of grain boundary motion, which was proposed by [Kobayashi-Warren-Carter, Phys. D, 140 (2000), 141-150]. This system is derived from a governing free energy, including a weighted total variation, and the weighted total variation bring down some nonstandard situations in mathematical expression of our system: a term of measure in the first equation; a singular diffusion with time-dependent weights.

The main objective of this talk is to give a certain definition method for solution of such system with nonstandards. Consequently, the existence of weak solutions of our system will be demonstrated with help from the general measure theory and the general theory of evolution equations governed by time-dependent subdifferentials.

For material related to this talk, click here.