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Landau-lifshitz Equations [Kietas viršelis]

(Inst Of Applied Physics & Computational Mathematics, China), (South China Normal Univ, China)
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This introduction to Landau-Lifshitz equations and Landau-Lifshitz-Maxwell equations begins with the work by Yulin Zhou and Boling Guo in the early 1980s and includes most of the recent work done by this Chinese group since. The book focuses on aspects such as the existence of weak solutions in multiple dimensions, existence and uniqueness of smooth solutions in one dimension, relations with harmonic map heat flows, partial regularity, and long time behaviors. The book can serve as a reference for those who are interested in partial differential equations, geometric analysis, and mathematical physics. It may also be used as an advanced textbook by graduate students in these fields. Guo is affiliated with the Beijing Institute of Applied Physics and Computational Mathematics, China. Ding is affiliated with South China Normal University. There is no subject index. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)
Preface v
Spin Waves and Equations of Ferromagnetic Spin Chain
1(34)
Physics Background for the Equations of Ferromagnetic Spin Chain
1(2)
A Simple Derivation of Landau-Lifshitz Equation
3(7)
Equations for the Antiferromagnets
10(2)
Spin Waves in Ferromagnets
12(10)
Spin Waves in Antiferromagnets
22(12)
Bibliography Comments
34(1)
Integrability of Heisenberg Chain
35(18)
Spin Waves and Solitary Waves
35(5)
Geometric Representation for the Landau-Lifshitz Equations
40(3)
Inhomogeneous Heisenberg Chain
43(3)
Spherical (Cylindrical) Symmetric Heisenberg Equations of Ferromagnetic Spin Chain
46(6)
Bibliography Comments
52(1)
One-Dimensional Landau-Lifshitz Equations
53(70)
Initial Boundary Value Problem of One-dimensional Ferromagnetic Spin Chain Equations
53(12)
Nonlinear Initial-boundary Value Problem for the System of Ferromagnetic Spin Chain
65(22)
Smooth Solution for the Ferromagnetic Spin Chain Systems
87(12)
Smooth Solution for the 1D Inhomogeneous Heisenberg Chain Equations
99(15)
Measure-Valued Solution to the Strongly Degenerate Compressible Heisenberg Chain Equations
114(7)
Bibliography Comments
121(2)
Landau-Lifshitz Equations and Harmonic Maps
123(118)
Weak Solution to Multidimensional Ferromagnetic Spin Chain Equations
123(14)
Landau-Lifshitz Equations on Riemannian Manifold and Harmonic Maps
137(21)
Generalized L-L Systems and Harmonic Maps
158(14)
Regularity of Weak Solutions to the Two-Dimensional Landau-Lifshitz Equations
172(9)
Ginzburg-Landau Approximation to Landau-Lifshitz Equations
181(21)
Smooth Solution and Decay Estimates to the L-L System with Small Initial Data in Higher Dimensions
202(15)
Radial Solution
217(22)
Bibliography Comments
239(2)
Landau-Lifshitz-Maxwell Equations
241(92)
Global Weak Solution in Three Dimensions
241(14)
Global Smooth Solution in One or Two Dimensions with Small Initial Data
255(13)
Global Smooth Solution to One-Dimensional L-L-M with Large Data
268(13)
Global Weak Solution to L-L-M System on Riemannian Manifold
281(10)
Partial Regularity for Stationary Solutions to L-L-M Equations
291(18)
Weak Solutions to Landau-Lifshitz-Maxwell Equations with Polarization
309(22)
Bibliography Comments
331(2)
Long Time Behavior of Solutions to the System of Ferromagnetic Spin Chain
333(60)
Existence and Stability of Steady State Solutions
333(3)
Asymptotic Behavior of L L Equations
336(8)
Approximate Inertial Manifold for One-Dimensional L-L Equations
344(10)
Attractor of Landau-Lifshitz Equations on Riemannian Manifold
354(14)
The Attractors for Landau-Lifshitz-Maxwell Equations
368(23)
Bibliography Comments
391(2)
Bibliography 393