具有多向效应场的二维柱对称Landau-Lifshitz方程静态解的存在性

Existence of a static solution of the 2D cylindrical symmetric Landau-Lifshitz equation with the multi-directional effective field

柱对称非线性LL方程全局弱解的存在性问题是当前铁磁链方程的研究热点之一.研究具有多向效应场的LL方程(方程GLL)静态解的存在性问题具有一定的理论及实际应用价值,尤其二维柱对称情形.主要考虑二维柱对称LL方程(方程HLZ)静态解的存在性,首先将直角坐标系下的方程GLL变换为柱坐标系下的方程HLZ,其次给出方程HLZ的显示静态解,最后应用Schauder不动点定理证明方程HLZ静态解的存在性.

This research proves the existence of a static solution of the 2 D cylindrical symmetric Landau-Lifshitz equation with the multi-directional effective field. Firstly, the Landau-Lifshitz equation in the rectangular coordinate system is transformed into the 2 D cylindrical symmetric Landau-Lifshitz equation. Secondly, the explicit static solution of 2 D cylindrical symmetric Landau-Lifshitz is given. Finally, the existence of a static solution is proved by using the Schauder fixed-point theorem.