TY - JOUR
T1 - Weak and Smooth Global Solution for Landau-Lifshitz-Bloch-Maxwell Equation
AU - Guo , Boling
AU - Han , Yongqian
AU - Huang , Daiwen
AU - Li , Fangfang
JO - Annals of Applied Mathematics
VL - 1
SP - 1
EP - 30
PY - 2020
DA - 2020/08
SN - 36
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/18063.html
KW - Landau-Lifshitz-Bloch-Maxwell equation, global solution, paramagnetic-ferromagnetic transition, temperature-dependent magnetic theory, Landau-Lifshitz theory.
AB - <p style="text-align: justify;">This paper is devoted to investigating the existence and uniqueness of the
solution of Landau-Lifshitz-Bloch-Maxwell equation. The Landau-Lifshitz-Bloch-Maxwell equation, which fits well for a wide range of temperature, is
used to study the dynamics of magnetization vector in a ferromagnetic body.
If the initial data is in ($H$<sup>1</sup>, $L$<sup>2</sup>, $L$<span style="text-align: justify;"><sup>2</sup></span>), the existence of the global weak solution
is established. If the initial data is in ($H$<sup>$m$</sup><sup>+1</sup>, $H$<sup>$m$</sup>, <span style="text-align: justify;"></span><span style="text-align: justify;">$H$</span><sup style="text-align: justify; white-space: normal;">$m$</sup><sup><span style="text-align: justify; font-size: 13.3333px;"></span></sup>) ($m$ ≥ 1), the existence
and uniqueness of the global smooth solution are established.</p>