Large deviations and transitions between equilibria for stochastic Landau-Lifshitz-Gilbert equation

Weak solutions of the Stochastic Landau–Lifshitz–Gilbert Equations with nonzero anisotrophy energy

“…In particular, our results give an alternative proof of the existence result from Brzeźniak, Goldys and Jegaraj's paper [15], where large deviations principle for stochastic LLG equation on a 1-dimensional domain has been studied. This paper is organized as follows.…”

“…An essential feature of the model studies in [33] was the presence of anisotropy energy (while the exchange energy was absent). So far none of the papers, apart from [15] which treats only onedimensional domains, on the stochastic LLGEs considered nonzero anisotropy energy. Therefore there is a need to fill this literature gap and that is what we have achieved in the current work.…”

Strong solvability of regularized stochastic Landau–Lifshitz–Gilbert equation

“…This suggests the general strategy of proving the existence and uniqueness of a stochastically strong solution by first constructing a stochastically weak solution and then showing that the solution is pathwise unique. In dimension one, this approach has successfully been applied to (1.4) in [11].…”