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Existence of large solutions to the Landau-Lifshitz-Bloch equation. (English) Zbl 1462.35377

Summary: In this work we discuss existence of solutions of the Landau-Lifshitz-Bloch equation describing the dynamics of the magnetization for the whole range of the temperature. By using energy method we prove global existence of strong solutions for given initial data, existence of time-periodic solutions as well as existence of steady state solutions of the equation.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B10 Periodic solutions to PDEs
35D35 Strong solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
35G31 Initial-boundary value problems for nonlinear higher-order PDEs
82D40 Statistical mechanics of magnetic materials
78A30 Electro- and magnetostatics
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