Mathematical analysis for phase field models of grain boundary motions
Prof. Ken Shirakawa, Chiba University
Sala conferenze IMATI-CNR - Tuesday, December 1, 2015 h.15:00
Abstract. This study is based on the recent jointworks with Prof. H. Watanabe (Salesian Polytech., Japan), Prof. S. Moll (Univ. Valencia, Spain) and Prof. N. Yamazaki (Kanagawa Univ., Japan). The contents of the talk are largely divided in former part and latter part. In the former part, we overview the recent mathematical studies of phase- field models of grain boundary motions, called Kobayashi–Warren–Carter type systems. In either system, the modelling idea is originated in the study of [R. Kobayashi et al., Physica D, 140 (2000), 141–150], and hence, the main part is described by a gradient system of a free-energy, including an interfacial energy of weighted total-variation. On the other hand, the latter part is devoted to our latest result, concerned with anisotropic systems of Kobayashi–Warren–Carter types. Roughly summarized, the anisotropic systems are derived by taking into account the rotation effects of Wulff shapes, which work with the variations of crystalline orientations. Since the rotation effects will bring some quasi-variational situations, our anisotropic systems will contain additional difficulties compared with the previous (isotropic) versions. After the discussions of the modelling ideas and the existence results for the anisotropic systems, we conclude the talk by looking at problems in future and open questions.
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