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

Ken Shirakawa; Hiroshi Watanabe; Ken Shirakawa; Hiroshi Watanabe

doi:10.3934/Math.2017.1.161

AIMS Mathematics

2017, Volume 2, Issue 1: 161-194. doi: 10.3934/Math.2017.1.161

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

Ken Shirakawa ^{1
,
,},
Hiroshi Watanabe ²

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

Received: 22 October 2016 Accepted: 16 January 2017 Published: 08 March 2017

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.
- Non-isothermal grain boundary motion,
- Kobayashi–Warren–Carter type model,
- existence of L2-based solution,
- weighted total variation,
- time-discretization
Citation: Ken Shirakawa, Hiroshi Watanabe. Solvability for the non-isothermal Kobayashi–Warren–Carter system[J]. AIMS Mathematics, 2017, 2(1): 161-194. doi: 10.3934/Math.2017.1.161

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Abstract

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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