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

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.

Keywords

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