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

AIMS Mathematics

Ken Shirakawa¹  HiroshiWatanabe² 

[1] 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;

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

DOI  :  10.3934/Math.2017.1.161

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown