| Abstract: |
| In this talk, we consider a class of parabolic systems, which can be called \emph{quasilinear type Kobayashi--Warren--Carter systems}. Each constituent system is based on the mathematical model of grain boundary motion, proposed by [Kobayashi-et. al, Physica D., 140 (2000), 141--150], and the principal part of the system consists of a quasilinear diffusion equation of singular type, subject to the dynamic boundary condition. The objective of this study is to obtain a uniform mathematical method for the quasilinear type Kobayashi--Warren--Carter systems including dynamic boundary conditions. On this basis, we here address three issues, concerned with the qualitative properties of the systems. The first is to show the existence of solutions to the systems, including the rigorous expressions of solutions. The second is to show the continuous associations among the different systems. The final is to show the large time behavior of solutions. The three issues will be demonstrated in forms of the Main Theorems of this talk. |
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