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AIMS Mathematics, 2017, 2(1): 161-194. doi: 10.3934/Math.2017.1.161. Research article Special Issue

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Solvability for the non-isothermal Kobayashi–Warren–Carter system

1 Department of Mathematics, Faculty of Education, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan
2 Department of Computer Science and Intelligent Systems, Faculty of Engineering, Oita University, 700 Dannoharu, Oita, 870-1192, Japan

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Special Issue: Nonlinear Evolution PDEs, Interfaces and Applications

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In this paper, a system of parabolic type initial-boundary value problems are considered. The system (S)$_\nu$ is based on the non-isothermal model of grain boundary motion by ^[38], which was derived as an extending version of the ``Kobayashi--Warren--Carter model'' of grain boundary motion by ^[23]. Under suitable assumptions, the existence theorem of $ L^2 $-based solutions is concluded, as a versatile mathematical theory to analyze various Kobayashi--Warren--Carter type models.

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Keywords: Non-isothermal grain boundary motion; Kobayashi–Warren–Carter type model; existence of L2-based solution; weighted total variation; time-discretization

Citation: Ken Shirakawa, HiroshiWatanabe. Solvability for the non-isothermal Kobayashi–Warren–Carter system. AIMS Mathematics, 2017, 2(1): 161-194. doi: 10.3934/Math.2017.1.161

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