This study is based on recent joint works with Prof. H. Watanabe (Oita Univ., Japan) and Prof. S. Moll (Univ. Valencia, Spain). In this talk, we consider systems of evolution equations, known as “Kobayashi-Warren-Carter type systems”, which are based on phase-field model of grain boundary motions, proposed by Kobayashi et al [R. Kobayashi et al., Physica D, 140 (2000), 141–150]. In the preliminary part of the talk, we overview the previous works on Kobayashi-Warren-Carter type systems, concerned with the existence, large-time behavior, and so on. On the other hand, the principal part of the talk is devoted to the recent study, concerned with structural observations under one-dimensional settings of spatial domains. The focus of this talk is on a special kind of solution, named “crystalline solution”, which is to reproduce the structural characteristics in polycrystal body, exactly. The main results are concerned with the existence and uniqueness of the crystalline solution, and especially, these results answer some of open questions in the studies of Kobayashi-Warren-Carter type systems.

 

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