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Weak and smooth global solution for Landau-Lifshitz-Bloch-Maxwell equation. (English) Zbl 1463.35383

Summary: This paper is devoted to investigate 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 \(({H^{m+1}}, {H^m}, {H^m}) (m \ge 1)\), the existence and uniqueness of the global smooth solution are established.

MSC:

35N30 Overdetermined initial-boundary value problems for PDEs and systems of PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
35Q61 Maxwell equations
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