Theoretical Analysis And Numerical Similation Of A Class Of Solid-Solid Phase Transiton Models

Solid-solid phase transition is a very important topic in the research on metal alloys. Solid-solid phase transition models can be classified into the order parameter conserved one and non-conserved one. The order parameter conserved model is used to describe the phase transition of ceramics, while the non-conserved one describes the process of martenstic phase transition, such as shape-memory alloy. In this thesis, we discuss the models which are improved from the phase transition model proposed by Alber-Zhu.In this thesis, we only focus on the non-conserved phase transition model in1-dimensional case. We discuss the existence of the weak solution and give their numerical solutions of these models. To begin with, we discuss the existence of weak solution for the Dirichlet and Neumann initial boundary value problem of the phase transition model with4th-order Laplace term. Secondly, we consider the model with5th-order Laplace term. Then, we study the existence of the weak solution for the model with arbitrary integer order. At last, we simulate these models by finite difference method.