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.