### AIMS Mathematics

2017, Issue 1: 161-194. doi: 10.3934/Math.2017.1.161
Research article Special Issues

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

• 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.

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

### Related Papers:

• 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.

• © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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