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 |