Weak solutions of the Landau--Lifshitz--Bloch equation

2016/05/16 by Le, Kim Ngan · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.04898

Abstract

The Landau--Lifshitz--Bloch (LLB) equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components important for high-temperature applications. We study LLB equation in case the temperature raised higher than the Curie temperature. The existence of weak solution is showed and its regularity properties are also discussed. In this way, we lay foundations for the rigorous theory of LLB equation that is currently not available.

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• Error analysis of scalar auxiliary variable finite element methods for the Landau–Lifshitz–Bloch equation
• Time Optimal Control Problem for the Landau-Lifshitz-Bloch equation

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