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

[摘要] 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 subset of 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) (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] Landau-Lifshitz-Bloch;Quasilinear parabolic equation;Stochastic partial differential equations;Ferromagnetism