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math.AP2018★ 2 cited
A class of parabolic systems associated with optimal controls of grain boundary motions
Harbir Antil, Ken Shirakawa, Noriaki Yamazaki
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain b…
math.AP2014★ 9 cited
Phase-field systems for grain boundary motions under isothermal solidifications
Ken Shirakawa, Hiroshi Watanabe, Noriaki Yamazaki
Two main existence theorems are proved for two nonstandard systems of parabolic initial-boundary value problems. The systems are based on the "-- model" proposed by Kob…