Weak Solutions of a Stochastic Landau-Lifshitz-Gilbert Equation
Zdzisław Brzeźniak, Beniamin Gołdys, Terence Jegaraj · Applied Mathematics Research eXpress · 2012
We consider a Landau-Lifshitz-Gilber equation perturbed by a multiplicative space-dependent noise for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere . The regularity of weak solutions is also discussed. Our research is in response to the paper by Kohn et al. “Magnetic elements at finite temperature and large deviation theory.” Journal of Nonlinear Science 15 (2005): 223–53, which calls for the study of stochastic equations with spatially varying magnetization.