Global weak solutions to a phase-field model for motion of grain boundaries

Abstract

We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational forces. The higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open domain. The existence proof is valid in the one-dimensional case.

Weak Solutions to an Initial-Boundary Value Problem of a Consistent Three-phase-field Model

“…Steinbach, et al [2], in 1966, first established the multi-phase free energy functional for multi-phase systems. For the phase-field method, We refer, such as, to [3][4][5][6]. In addition, Tóth and Pusztai [7] proposed seven multi-phase-field criteria to describe a generalized multi-phase-field model for an arbitrary number of phases (or domains) in 2015.…”