Screen LibraryLandau-Lifshitz equations /
This is a comprehensive introduction to Landau-Lifshitz equations and Landau-Lifshitz-Maxwell equations, beginning with the work by Yulin Zhou and Boling Guo in the early 1980s and including most of the work done by this Chinese group led by Zhou and Guo since. The book focuses on aspects such as th...
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; Hackensack, N.J. : |
| Publication Dates: | 2008. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Frontiers of research with the Chinese Academy of Sciences ;
v. 1 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/6658#t=toc |
| Summary: |
This is a comprehensive introduction to Landau-Lifshitz equations and Landau-Lifshitz-Maxwell equations, beginning with the work by Yulin Zhou and Boling Guo in the early 1980s and including most of the work done by this Chinese group led by Zhou and Guo since. The book focuses on aspects such as the existence of weak solutions in multi dimensions, existence and uniqueness of smooth solutions in one dimension, relations with harmonic map heat flows, partial regularity and long time behaviors. The book is a valuable reference book 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. |
| Carrier Form: | 1 online resource (x,403pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 393-403) |
| ISBN: |
9812778764 (electronic bk.) 9789812778765 (electronic bk.) |
| CLC: | O241.82 |
| Contents: | 1. Spin waves and equations of ferromagnetic spin chain. 1.1. Physics background for the equations of ferromagnetic spin chain. 1.2. A simple derivation of Landau-Lifshitz equation. 1.3. Equations for the antiferromagnets. 1.4. Spin waves in ferromagnets. 1.5. Spin waves in antiferromagnets -- 2. Integrability of Heisenberg chain. 2.1. Spin waves and solitary waves. 2.2. Geometric representation for the Landau-Lifshitz equations. 2.3. Inhomogeneous Heisenberg chain. 2.4. Spherical (cylindrical) symmetric Heisenberg equations of ferromagnetic spin chain -- 3. One-dimensional Landau-Lifshitz equations. 3.1. Initial boundary value problem of one-dimensional ferromagnetic spin chain equations. 3.2. Nonlinear initial-boundary value problem for the system of ferromagnetic spin chain. 3.3. Smooth solution for the ferromagnetic spin chain systems. 3.4. Smooth solution for the 1D inhomogeneous Heisenberg chain equations. 3.5. Measure-valued solution to the strongly degenerate compressible Heisenberg chain equations -- 4. Landau-Lifshitz equations and harmonic maps. 4.1. Weak solution to multidimensional ferromagnetic spin chain equations. 4.2. Landau-Lifshitz equations on Riemannian manifold and harmonic maps. 4.3. Generalized L-L systems and harmonic maps. 4.4. Regularity of weak solutions to the two-dimensional Landau-Lifshitz equations. 4.5. Ginzburg-Landau approximation to Landau-Lifshitz equations. 4.6. Smooth solution and decay estimates to the L-L system with small initial data in higher dimensions. 4.7. Radial solution -- 5. Landau-Lifshitz-Maxwell equations. 5.1. Global weak solution in three dimensions. 5.2. Global smooth solution in one or two dimensions with small initial data. 5.3. Global smooth solution to one-dimensional L-L-M with large data. 5.4. Global weak solution to L-L-M system on Riemannian manifold. 5.5. Partial regularity for stationary solutions to L-L-M equations. 5.6. Weak solutions to Landau-Lifshitz-Maxwell equations with polarization -- Long time behavior of solutions to the system of ferromagnetic spin chain. 6.1. Existence and stability of steady state solutions. 6.2. Asymptotic behavior of L-L equations. 6.3. Approximate inertial manifold for one-dimensional L-L equations. 6.4. Attractor of Landau-Lifshitz equations on Riemannian manifold. 6.5. The attractors for Landau-Lifshitz-Maxwell equations. |