Two Dimensional Landau-Lifshitz Equations in Micromagnetism

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" Two Dimensional Landau-Lifshitz Equations in Micromagnetism "

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	151607
Doc. No	:	ET23399
Main Entry	:	XIAOMING XU
Title Proper	:	Two Dimensional Landau-Lifshitz Equations in Micromagnetism
Note	:	This document is digital این مدرک بصورت الکترونیکی می باشد
Abstract	:	Landau-Lifshitz equations are fundamental equations in the theory of ferromag-net ism. They describe the dynamics of the magnetization field inside ferromagneticmaterial. They were first derived by L. Landau and E. Lifshitz. In the thesis westudy the Landau-Lifshitz equations with a damping term. These equations form asystem of quasilinear parabolic equations. In the first part of the thesis, we studythe simplified Landau-Lifshitz equations in which only the term that comes fromexchange energy appears. We prove the existence, uniqueness and partial regularityfor the weak solution of the equations. Our proof is simpler and clearer than theproof given by other authors. We also give a detailed description of the behaviour ofthe solution near point singularities. In the second part of the thesis, we study thefull Landau-Lifshitz equations. The nonlocal term that comes from the self- inducedmagnetic field makes the equations hard to deal with by the conventional methodsfor parabolic equations. However, our method in the first part of the thesis canbe e-xtended without difficulty to prove the complete result of existence, uniquenessand partial regularity for the weak solution of the full Landau-Lifshitz equations. Inthe final part of the thesis, we discuss three dimensional Landau-Lifshitz equationsand some interesting open problems......-....,....-...,..tested for theQ1 PC1 bus cardBoth these projects mere sofixare des elopment efforts tonards contributing to dlfferentaspects of Roboucs and lZ1echatronics projects m the Controls and Roboucs Group..
Subject	:	Electericl tess
	:	برق
electronic file name	:	TL46638.pdf
Title and statement of responsibility and	:	Two Dimensional Landau-Lifshitz Equations in Micromagnetism [Thesis]