Some Results On Quantization Effect For A Ginzburg-Landau Type Functional

The Ginzburg-Landau equation is a mathematical model of simplification which constitutes system in engineering, and each kind of mode in the physics. It is used to describe some variables of statistics physics, which appear in the continuous phase transformation. The typical situation is researching the vortices'properties in the study of superconductivity, superfluidity or XY-magnetism.Different from the Ginzburg-Landau energy , we shall consider a variant form energy function: Its minimizer u_εin some function class satisfies the equation:whereΩbe a smooth, bounded simply connected domain in R~2. After scaling we haveIn chapter 1 we consider the condition of n = 2 , which u is a common solution .In chapter 2 we also consider the condition of n = 2 while u is a radial solution .In chapter 3 we consider the condition of n≥3, which u is a radial solution. In these three conditions, we have given some results on quantization effect for a Ginzburg-Landau type functional.