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Regular solutions for Landau-Lifschitz equation in $$\mathbb R^ 3$$. (English) Zbl 1084.35519
Summary: The authors prove local existence, global existence with small data and uniqueness of regular solutions for Landau-Lifschitz equations. Furthermore they establish local existence and uniqueness for a system coupling Maxwell and Landau-Lifschitz equations arising from Micromagnetism theory.

##### MSC:
 35K55 Nonlinear parabolic equations 35Q60 PDEs in connection with optics and electromagnetic theory 82D40 Statistical mechanical studies of magnetic materials 35K15 Initial value problems for second-order parabolic equations