二维Landau-Lifshitz静态方程组的渐近性质

Asymptotics for Landau-Lifshitz Equailifrium Systems in Two Dimensions

在本文中，我们讨论了ｕ∧（－Δｕ＋λ（ｕ，ｎ）ｎ）＝０，｜ｕ｜＝１，ｘ∈Ｂ１和ｕ＝（ｘ１，ｘ２，０）ｘ∈Ｂ１的轴对称解ｕλ的渐近行为，其中Ｂ１是Ｒ２中单位圆，ｕ＝（ｕ１，ｕ２，ｕ３）．我们证明了ｕλｕ∞在Ｈ２Ｂ１＼Ｂε，Ｒ３中．

In this paper, we describe the asymptotic behavior, as λ+∞ , of axially symmetric solutions u λ for the problem: u∧(-Δu+λ(u,n)n) =0 , |u|=1 , x∈B 1 and u=(x 1,x 2,0) , x∈B 1 , where B 1 is the unit ball in R 2 , u=(u 1,u 2,u 3) , n=(0,0,1) . We prove here that u λ convergent u ∞ in H 2(B 1\B ε, R 3) .