Existence of weak solutions and numerical simulations for a new
phase-field model with periodic boundary conditions
Abstract
This article is concerned with an initial-boundary value problem (IBVP)
for a new phase-field model describing the evolution of structural phase
transition in elastically deformable solid materials. The model consists
of an elliptic-parabolic system in which the displacement field and the
order parameter both satisfy periodic boundary conditions. We prove the
existence of global solutions to this IBVP by applying the method of
continuation of local solutions and perform numerical simulations to
investigate the microstructure evolution of MnNi alloys by using this
new phase-field model.