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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$$m$) ($m$ ≥ 1), the existence and uniqueness of the global smooth solution are established.
}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18063.html} }This paper is devoted to investigating the existence and uniqueness of the solution of Landau-Lifshitz-Bloch-Maxwell equation. The Landau-Lifshitz-Bloch-Maxwell equation, which fits well for a wide range of temperature, is used to study the dynamics of magnetization vector in a ferromagnetic body. If the initial data is in ($H$1, $L$2, $L$2), the existence of the global weak solution is established. If the initial data is in ($H$$m$+1, $H$$m$, $H$$m$) ($m$ ≥ 1), the existence and uniqueness of the global smooth solution are established.