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arXiv · 1901.02973

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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Abstract

The Landau--Lifshitz--Bloch equation perturbed by a space-dependent noise was proposed in Garanin 1991 as a model for evolution of spins in ferromagnatic 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 $D\subset \mathbb R^d$, $d=1,2,3$, 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.

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Zdzislaw Brzeźniak, Beniamin Goldys, Kim Ngan Le. 2019-01-10. Existence of a unique solution and invariant measures for the stochastic Landau--Lifshitz--Bloch equation. https://arxiv.org/abs/1901.02973

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