Landau Lifshitz Equations (Frontiers of Research With the Chinese Academy of Sciences)

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. Contents: Spin Waves and Equations of Ferromagnetic Spin Chain; Integrability of Heisenberg Chain; One-Dimensional Landau Lifshitz Equations; Landau Lifshitz Equations and Harmonic Maps; Landau Lifshitz Maxwell Equations; Long Time Behavior of Solutions to the System of Ferromagnetic Spin Chain.