Viscosity Solutions To A Neumann Initial Boundary Value Problem Of A New Phase-field Model For Solid-solid Phase Transitions

Materials technology breakthrough tends to speed up the development of human society,and materials science is an interdisciplinary field.The microstructure of a material determines its physical properties and performance,under certain conditions,when the atoms of matter are rearranged,the shape and structure of matter will change.This process is called phase transition.According to the interface thickness,the phase transition model can be divided into sharp interface model and phase field model.The phase field model are divided into two kinds: order parameter is conserved and not conserved.We shall study an initial-boundary value problem of a new phase field model,which is a degenerate parabolic equation coupled to a linear elasticity sub-system,used to describe the solid-solid phase transitions in elastically deformable solid materials.This model was proposed by Alber and Zhu in 2006 [1],and the order parameter in this model is not conserved.We first establish a series of approximate solutions to the initial boundary value problem,and by passing the approximate solutions to the limit,then prove that the viscosity solutions to this initial boundary value problem exist,in a one dimensional case.