论文标题
Landau-Lifshitz方程的均质化
Homogenization of the Landau-Lifshitz equation
论文作者
论文摘要
在本文中，我们考虑使用具有高度振荡的材料系数的Landau-Lifshitz方程，并具有$ \ varepsilon $建模铁磁复合材料。我们为问题和相应的校正器得出了均质化解决方案的方程，并获得了精确溶液和均质溶液之间差的估计以及对溶液的校正近似值。 $ \ varepsilon $在时间$ o（\ varepsilon^σ）$中的收敛速率和$ 0 \leqσ\ leq 2 $在sobolev norm $ $ h^q $中给出，其中$ q $受到详细的landau-lifshitz方程和本国基础的详细解决方案的限制。费率取决于$ q $，$σ$和校正数的数量。
In this paper, we consider homogenization of the Landau-Lifshitz equation with a highly oscillatory material coefficient with period $\varepsilon$ modeling a ferromagnetic composite. We derive equations for the homogenized solution to the problem and the corresponding correctors and obtain estimates for the difference between the exact and homogenized solution as well as corrected approximations to the solution. Convergence rates in $\varepsilon$ over times $O(\varepsilon^σ)$ with $0\leq σ\leq 2$ are given in the Sobolev norm $H^q$, where $q$ is limited by the regularity of the solution to the detailed Landau-Lifshitz equation and the homogenized equation. The rates depend on $q$, $σ$ and the the number of correctors.
