The Ferromagnetic Chain Equations at High Temperatures (eBook, PDF)
Analysis and Applications of the Landau-Lifshitz-Bloch Equations
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This book presents a comprehensive exploration of the mathematical theory and recent advances related to the ferromagnetic chain equations at high temperatures, with a particular focus on the Landau-Lifshitz-Bloch (LLB) equation and its extensions. More specifically, the work addresses key topics, including the LLB equation, the coupled Maxwell-LLB system, temperature-dependent LLB models, nonlinear electron polarization systems, and stochastic and fractional LLB equations. It highlights a series of innovative results: ranging from the existence of weak and smooth solutions to the construction...
This book presents a comprehensive exploration of the mathematical theory and recent advances related to the ferromagnetic chain equations at high temperatures, with a particular focus on the Landau-Lifshitz-Bloch (LLB) equation and its extensions. More specifically, the work addresses key topics, including the LLB equation, the coupled Maxwell-LLB system, temperature-dependent LLB models, nonlinear electron polarization systems, and stochastic and fractional LLB equations. It highlights a series of innovative results: ranging from the existence of weak and smooth solutions to the construction of global attractors and the analysis of periodic behaviors. By integrating rigorous mathematical derivations with underlying physical principles, it serves as a valuable reference for researchers in mathematics, physics, and materials science.
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