Weak Solutions of the Stochastic Landau-lifshitz-gilbert Equation
نویسنده
چکیده
Abstract. The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative spacedependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere S. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert equation.
منابع مشابه
Convergence of an Implicit Finite Element Method for the Landau-Lifshitz-Gilbert Equation
The Landau-Lifshitz-Gilbert equation describes dynamics of ferromagnetism, where strong nonlinearity, nonconvexity are hard to tackle: so far, existing schemes to approximate weak solutions suffer from severe time-step restrictions. In this paper, we propose an implicit fully discrete scheme and verify unconditional convergence.
متن کاملNumerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation
The Landau-Lifshitz-Gilbert equation describes magnetic behavior in ferromagnetic materials. Construction of numerical strategies to approximate weak solutions for this equation is made difficult by its top order nonlinearity and nonconvex constraint. In this paper, we discuss necessary scaling of numerical parameters and provide a refined convergence result for the scheme first proposed by Alo...
متن کاملConvergence result for the constraint preserving mid-point scheme for micromagnetism
An important progress was recently done in numerical approximation of weak solutions to a micromagnetic model equation. The problem with the nonconvex sideconstraint of preserving the length of the magnetization was tackled by using reduced integration. Several schemes were proposed and their convergence to weak solutions was proved. All schemes were derived from the Landau-Lifshitz-Gilbert for...
متن کاملLandau-Lifshitz-Slonczewski Equations: Global Weak and Classical Solutions
We consider magnetization dynamics under the influence of a spin-polarized current, given in terms of a spin-velocity field v, governed by the following modification of the Landau– Lifshitz–Gilbert equation ∂m ∂t + v · ∇m = m × (α ∂m ∂t + β v · ∇m − Δm), called the Landau– Lifshitz–Slonczewski equation. We focus on the situation of magnetizations defined on the entire Euclidean space m(t) : R3 ...
متن کاملNumerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretization schemes.
We introduce a numerical method to integrate the stochastic Landau-Lifshitz-Gilbert equation in spherical coordinates for generic discretization schemes. This method conserves the magnetization modulus and ensures the approach to equilibrium under the expected conditions. We test the algorithm on a benchmark problem: the dynamics of a uniformly magnetized ellipsoid. We investigate the influence...
متن کامل