Communications in Mathematical Sciences

Volume 21 (2023)

Number 6

The initial-boundary value problem for the Landau–Lifshitz equation with Gilbert damping term

Pages: 1727 – 1742

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n6.a13

Authors

Qi Guo (Graduate School of China Academy of Engineering Physics, Beijing, China)

Yamin Xiao (Graduate School of China Academy of Engineering Physics, Beijing, China)

Abstract

In this paper, we establish the existence of global smooth solutions for the Landau–Lifshitz type system on a finite interval $[0,L]$. The proof is based on the technique of finite difference-differential and a priori estimates. Our result matches the known result on periodic boundary condition in $[\href{https://doi.org/10.3934/dcds.1999.5.729}{7}]$.

Keywords

Landau–Lifshitz system, initial-boundary value problem, smooth solutions

2010 Mathematics Subject Classification

35B65, 35Q60

Full Text (PDF format)

Received 24 November 2022

Accepted 15 December 2022

Published 22 September 2023