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

doi:10.1007/s10483-022-2915-9

Abstract

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.

Key words: solid-solid phase transition, phase-field model, Galerkin method, weak solutions

2010 MSC Number:

35K65
82B26

Zixian ZHU, Boling GUO, Shaomei FANG. Global weak solutions to a phase-field model for motion of grain boundaries. Applied Mathematics and Mechanics (English Edition), 2022, 43(11): 1777-1792.

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