Description
Book SynopsisThis 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.
Table of ContentsPhysical Background of Landau-Lifshitz Equations and Landau-Lifshitz-Maxwell Equations; Existence of Weak Solutions to Landau-Lifshitz Equations and Landau-Lifshitz-Maxwell Equations in Multi-Dimensions; Existence and Uniqueness of Smooth Solutions for Landau-Lifshitz Equations with or without Gilbert Damping in One Dimension; Discovery of the Relations with Harmonic Map Heat Flows and Partial Regularity for Chen-Struwe Solutions on Two Dimensional Riemannian Manifolds; Partial Regularity for Weak Solutions to Landau-Lifshitz Equations and Landau-Lifshitz-Maxwell Equations in Higher Dimensions; Long Time Behaviors and Attractors.
