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Volume 36, Issue 1
Weak and Smooth Global Solution for Landau-Lifshitz-Bloch-Maxwell Equation

Boling Guo, Yongqian Han, Daiwen Huang & Fangfang Li

Ann. Appl. Math., 36 (2020), pp. 1-30.

Published online: 2020-08

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  • Abstract

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$1, $L$2, $L$2), the existence of the global weak solution is established. If the initial data is in ($H$$m$+1, $H$$m$, $H$$m$) ($m$ ≥ 1), the existence and uniqueness of the global smooth solution are established.

  • Keywords

Landau-Lifshitz-Bloch-Maxwell equation, global solution, paramagnetic-ferromagnetic transition, temperature-dependent magnetic theory, Landau-Lifshitz theory.

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COPYRIGHT: © Global Science Press

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@Article{AAM-36-1, author = {Guo , BolingHan , YongqianHuang , Daiwen and Li , Fangfang}, title = {Weak and Smooth Global Solution for Landau-Lifshitz-Bloch-Maxwell Equation}, journal = {Annals of Applied Mathematics}, year = {2020}, volume = {36}, number = {1}, pages = {1--30}, abstract = {

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$1, $L$2, $L$2), the existence of the global weak solution is established. If the initial data is in ($H$$m$+1, $H$$m$, $H$$m$) ($m$ ≥ 1), the existence and uniqueness of the global smooth solution are established.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18063.html} }
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 -

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$1, $L$2, $L$2), the existence of the global weak solution is established. If the initial data is in ($H$$m$+1, $H$$m$, $H$$m$) ($m$ ≥ 1), the existence and uniqueness of the global smooth solution are established.

Guo , BolingHan , YongqianHuang , Daiwen and Li , Fangfang. (2020). Weak and Smooth Global Solution for Landau-Lifshitz-Bloch-Maxwell Equation. Annals of Applied Mathematics. 36 (1). 1-30. doi:
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