论文标题
薄膜上的Landau-Lifshitz-Bloch方程
The Landau-Lifshitz-Bloch equation on the thin film
论文作者
论文摘要
我们考虑了三维铁磁膜上Landau-Lifshitz-Bloch方程的初始边界值问题，其中有效场包含由Maxwell方程控制的杂散场，而交换场包含交换常数。在本文中，我们通过使用Faedo-Galerkin近似方法来建立方程弱解的存在。当膜厚度在适当的紧凑条件下趋于零时，我们还以数学上的方式得出其二维极限方程。此外，我们获得了一个方程式，可以更好地描述在高温下厚度可忽略不计的铁磁膜的磁动力学行为。
We consider the initial boundary value problem of Landau-Lifshitz-Bloch equation on three-dimensional ferromagnetic films, where the effective field contains the stray field controlled by Maxwell equation and the exchange field contains exchange constant. In this paper, we establish the existence of weak solutions of the equation by using the Faedo-Galerkin approximation method. We also derive its two-dimensional limit equation in a mathematically rigorous way when the film thickness tends to zero under appropriate compactness conditions. Moreover, we obtain an equation that can better describe the magnetic dynamic behavior of ferromagnetic films with negligible thickness at high temperature.
