Solutions To A Phase-field Model For Solid-solid Phase Transitions Driven By Configurational Forces

Solid-solid phase transition is a very important topic in the research on metal alloys.According to the thickness of the model interface,the phase transformation model can be divided into two types:the sharp interface model and the phase field model.The phase field model is based on the phase field method,which describes the microstructure evolution of the system.Also two cases are considered:the order parameter is conserved and not conserved.Phase field method is a young discipline and a powerful tool to simulate the microstructure evolution of various substances.The study of phase field model has great impetus to the development of material science.It not only has important significance in theory,but also has important application value in practice.Based on the Alber-Zhu model that the order parameter is non-conserved,we ignore its elasticity effect,and only study the solid-solid phase transition effect.We prove the existence of weak solutions to the one-dimensional initial-boundary value problem with Neumann boundary conditions for a model system comprising of partial differential equa-tions by the idea of Galerkin approximation.One application of this model is to describe martensitic phase transitions occurring in,e.g.,shape memory alloys.We shall also inves-tigate large-time behavior of the solutions,and obtain that S-S? 0 in L?(?),as t??,where ?=(a,d)and S denotes the mean value of S on ?.