Weak solutions of the Landau–Lifshitz–Bloch equation

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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.

Original languageEnglish
Pages (from-to)6699-6717
Number of pages19
JournalJournal of Differential Equations
Issue number12
Publication statusPublished - 15 Dec 2016
Externally publishedYes


  • Ferromagnetism
  • Landau–Lifshitz–Bloch
  • Quasilinear parabolic equation

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