Study On Radial Solution Of Landau - Lifschitz Equation

We study the asymptotic behavior of radial solutions of a Landau-Lifschitz type equation in two dimensions. Such an equation is associated with the study of ferromagnets and antiferromagnets. In addition, it is helpful to understand the singularities of the heat flow of harmonic maps. First, we establish the uni-form energy estimation for the radial solution of uε in a domain far away from the zeros. When the parameter ε goes to zero, we obtain the convergence of uε to (x/|x|,0)(which is a harmonic map), and the zeros of uε are located near the line segment{0}×[0, T].