TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=85087213853&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2020.06.061
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 -