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

Zdzislaw Brzeźniak; Beniamin Goldys; Kim Ngan Le

doi:10.1016/j.jde.2020.06.061

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

Zdzislaw Brzeźniak
, Beniamin Goldys
, Kim Ngan Le

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

28 Citations (Scopus)

Abstract

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⊂R^d, 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 language	English
Pages (from-to)	9471-9507
Number of pages	37
Journal	Journal of Differential Equations
Volume	269
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2020.06.061
Publication status	Published - 15 Nov 2020

Keywords

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

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10.1016/j.jde.2020.06.061

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

abstract = "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",

keywords = "Ferromagnetism, Landau–Lifshitz–Bloch, Quasilinear parabolic equation, Stochastic partial differential equations",

author = "Zdzislaw Brze{\'z}niak and Beniamin Goldys and Le, \{Kim Ngan\}",

year = "2020",

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T1 - Existence of a unique solution and invariant measures for the stochastic Landau–Lifshitz–Bloch equation

AU - Brzeźniak, Zdzislaw

AU - Goldys, Beniamin

AU - Le, Kim Ngan

PY - 2020/11/15

Y1 - 2020/11/15

N2 - 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

AB - 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

KW - Ferromagnetism

KW - Landau–Lifshitz–Bloch

KW - Quasilinear parabolic equation

KW - Stochastic partial differential equations

UR - https://www.scopus.com/pages/publications/85087213853

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DO - 10.1016/j.jde.2020.06.061

M3 - Article

AN - SCOPUS:85087213853

SN - 0022-0396

VL - 269

SP - 9471

EP - 9507

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 11

ER -

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

Abstract

Keywords

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