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Li, Jingna

A two-dimensional Landau-Lifshitz model in studying thin film micromagnetics. (English) Zbl 1165.74019

Abstr. Appl. Anal. 2009, Article ID 603591, 13 p. (2009).
Summary: The paper is concerned with a two-dimensional Landau-Lifshitz equation which was first raised by A. DeSimone et al. [Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 457, No. 2016, 2983–2991 (2001; Zbl 1065.74028)], and so forth, when studying thin film micromagnetics. We get the existence of a local weak solution by approximating it with a higher-order equation. Penalty approximation and semigroup theory are employed to deal with the higher-order equation.

MSC:

74F15 Electromagnetic effects in solid mechanics
74K35 Thin films
35Q72 Other PDE from mechanics (MSC2000)
35Q60 PDEs in connection with optics and electromagnetic theory
82D40 Statistical mechanics of magnetic materials

Keywords:

penalty approximation; existence; local weak solution; semigroup theory

Citations:

Zbl 1065.74028
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References:

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