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| This study is based on the line of jointworks with Prof. S. Moll (Univ. Valencia, Spain), Prof. H. Watanabe (Salesian Polytechnic, Japan) and Prof. N. Yamazaki (Kanagawa Univ., Japan).
In this talk, a coupled system of parabolic type variational inequalities is considered. On the basis of the modelling method of [Kobayashi, RIMS Kokyuroku, 1210 (2001), 68-77], this system is derived as a gradient system of a governing free-energy. So, roughly summarized, our system is largely consists of two gradient flows: the Allen-Cahn type equation for the isothermal solidification; the Kobayashi-Warren-Carter type system for the grain boundary motion, originated from [Kobayashi-Warren-Carter, Phys. D, 140 (2000), 141-150].
The focus in this talk is on a special kind of solution, named as "energy-dissipative solution", which realizes the dissipation of the free-energy in time. Consequently, the existence of energy-dissipative solution and some related topics will be presented as the main results of this talk. |
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