On a model of magnetization dynamics with vertical spin stiffness

Abstract

We consider a mathematical model describing magnetization dynamics with vertical spin stiffness. The model consists of a modified form of the Landau-Lifshitz-Gilbert equation for the evolution of the magnetization vector in a rigid ferromagnet. The modification lies in the presence in the effective field of a nonlinear term describing vertical spin stiffness. We prove the global existence of weak solutions to the model by using the Faedo-Galerkin method and discuss the limit of the obtained solutions as the vertical spin stiffness parameter tends to zero. MSC: 78A25; 35Q60; 35B40

Weak Solutions to a Landau–Lifshitz Equation with a p -Laplacian Operator as an Exchange Field

“…e work [4] addressed global existence of weak solution to a modern structure of the Landau-Lifshitz-Gilbert equation. e modi cation lies in occurrence of the e ective eld of a nonlinear term describing vertical spin sti ness and discuss the limit of got results as a vertical spin sti ness parameter converges to zero.…”