2022/08/13 by Yuxun He, He, Yuxun, Huaqiao Wang +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fluid Dynamics and Thin Films
paper · pdf · doi:10.48550/arxiv.2208.06558
openalex publication_date 2022/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.