Existence of a unique solution and invariant measures for the stochastic Landau–Lifshitz–Bloch equation

Zdzislaw Brzeźniak, Beniamin Goldys, Kim Ngan Le

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2 Citations (Scopus)


The Landau–Lifshitz–Bloch equation perturbed by a space-dependent noise was proposed in [10] as a model for evolution of spins in ferromagnetic materials at the full range of temperatures, including the temperatures higher than the Curie temperature. In the case of a ferromagnet filling a bounded domain D⊂Rd, d=1,2,3, we show the existence of strong (in the sense of PDEs) martingale solutions. Furthermore, in cases d=1,2 we prove uniqueness of pathwise solutions and the existence of invariant measures.1

Original languageEnglish
Pages (from-to)9471-9507
Number of pages37
JournalJournal of Differential Equations
Issue number11
Publication statusPublished - 15 Nov 2020


  • Ferromagnetism
  • Landau–Lifshitz–Bloch
  • Quasilinear parabolic equation
  • Stochastic partial differential equations

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